حلول الأسئلة
السؤال
بيّن ما إذا كانت كل من المتتابعتين الآتيتين هندسية أم لا؟
الحل
نعم.
شاهد حلول جميع الاسئلة
حل أسئلة تأكد
بيّن ما إذا كانت كل من المتتابعتين الآتيتين حسابية أم لا؟
1) format('truetype')%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%3C%2Fstyle%3E%3C%2Fdefs%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%224.5%22%20y%3D%2216%22%3E8%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1912723e55f2af848fec4212e09%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2211.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1912723e55f2af848fec4212e09%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2221.5%22%20y%3D%2216%22%3E%26%23x2212%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2233.5%22%20y%3D%2216%22%3E2%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1912723e55f2af848fec4212e09%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2240.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1912723e55f2af848fec4212e09%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2250.5%22%20y%3D%2216%22%3E%26%23x2212%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2267.5%22%20y%3D%2216%22%3E12%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1912723e55f2af848fec4212e09%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2278.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1912723e55f2af848fec4212e09%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2288.5%22%20y%3D%2216%22%3E%26%23x2212%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22105.5%22%20y%3D%2216%22%3E22%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1912723e55f2af848fec4212e09%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22116.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1912723e55f2af848fec4212e09%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22125.5%22%20y%3D%2216%22%3E%26%23x2026%3B%3C%2Ftext%3E%3C%2Fsvg%3E)
نعم.
2) format('truetype')%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%3C%2Fstyle%3E%3C%2Fdefs%3E%3Ctext%20font-family%3D%22math1258f61e431a13dee47ee630c68%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%226.5%22%20y%3D%2216%22%3E%26%23x2212%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2222.5%22%20y%3D%2216%22%3E19%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1258f61e431a13dee47ee630c68%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2233.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1258f61e431a13dee47ee630c68%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2243.5%22%20y%3D%2216%22%3E%26%23x2212%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2260.5%22%20y%3D%2216%22%3E12%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1258f61e431a13dee47ee630c68%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2271.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1258f61e431a13dee47ee630c68%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2281.5%22%20y%3D%2216%22%3E%26%23x2212%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2293.5%22%20y%3D%2216%22%3E5%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1258f61e431a13dee47ee630c68%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22100.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22107.5%22%20y%3D%2216%22%3E2%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1258f61e431a13dee47ee630c68%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22114.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%22121.5%22%20y%3D%2216%22%3E9%3C%2Ftext%3E%3C%2Fsvg%3E)
نعم.
أوجد الحدود الأربعة التالية في كل من المتتابعتين الحسابيتين الآتيتين، ثم مثل الحدود السبعة الأولى بيانياً.
3) format('truetype')%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%3C%2Fstyle%3E%3C%2Fdefs%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%224.5%22%20y%3D%2216%22%3E6%3C%2Ftext%3E%3Ctext%20font-family%3D%22math10eb3775255ffdaa027da963d8b%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2211.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2223.5%22%20y%3D%2216%22%3E18%3C%2Ftext%3E%3Ctext%20font-family%3D%22math10eb3775255ffdaa027da963d8b%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2234.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2246.5%22%20y%3D%2216%22%3E30%3C%2Ftext%3E%3Ctext%20font-family%3D%22math10eb3775255ffdaa027da963d8b%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2257.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22math10eb3775255ffdaa027da963d8b%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2266.5%22%20y%3D%2216%22%3E%26%23x2026%3B%3C%2Ftext%3E%3C%2Fsvg%3E)
4) format('truetype')%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%3C%2Fstyle%3E%3C%2Fdefs%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%229.5%22%20y%3D%2216%22%3E15%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1912723e55f2af848fec4212e09%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2220.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2227.5%22%20y%3D%2216%22%3E6%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1912723e55f2af848fec4212e09%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2234.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1912723e55f2af848fec4212e09%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2244.5%22%20y%3D%2216%22%3E%26%23x2212%3B%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2256.5%22%20y%3D%2216%22%3E3%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1912723e55f2af848fec4212e09%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2263.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1912723e55f2af848fec4212e09%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2272.5%22%20y%3D%2216%22%3E%26%23x2026%3B%3C%2Ftext%3E%3C%2Fsvg%3E)
5) توفير: يوفر سعيد 250 ريالاً شهرياً، فإذا كان معه 1000 ريال في البداية فأوجد ما يلي:
a) المبلغ الذي سيصبح معه بعد مرور 8 أشهر.
3000 ريال.
b) الوقت الذي يحتاج إليه ليصبح معه 7250 ريالاً، إذا استمر في التوفير بالطريقة ذاتها.
25 شهر.
بيّن ما إذا كانت كل من المتتابعتين الآتيتين هندسية أم لا؟
6) format('truetype')%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%3C%2Fstyle%3E%3C%2Fdefs%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%224.5%22%20y%3D%2216%22%3E4%3C%2Ftext%3E%3Ctext%20font-family%3D%22math10eb3775255ffdaa027da963d8b%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2211.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2223.5%22%20y%3D%2216%22%3E12%3C%2Ftext%3E%3Ctext%20font-family%3D%22math10eb3775255ffdaa027da963d8b%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2234.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2246.5%22%20y%3D%2216%22%3E36%3C%2Ftext%3E%3Ctext%20font-family%3D%22math10eb3775255ffdaa027da963d8b%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2257.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2273.5%22%20y%3D%2216%22%3E108%3C%2Ftext%3E%3Ctext%20font-family%3D%22math10eb3775255ffdaa027da963d8b%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2289.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22math10eb3775255ffdaa027da963d8b%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2298.5%22%20y%3D%2216%22%3E%26%23x2026%3B%3C%2Ftext%3E%3C%2Fsvg%3E)
نعم.
7) format('truetype')%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%3C%2Fstyle%3E%3C%2Fdefs%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%224.5%22%20y%3D%2216%22%3E7%3C%2Ftext%3E%3Ctext%20font-family%3D%22math10eb3775255ffdaa027da963d8b%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2211.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2223.5%22%20y%3D%2216%22%3E14%3C%2Ftext%3E%3Ctext%20font-family%3D%22math10eb3775255ffdaa027da963d8b%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2234.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2246.5%22%20y%3D%2216%22%3E21%3C%2Ftext%3E%3Ctext%20font-family%3D%22math10eb3775255ffdaa027da963d8b%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2257.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2269.5%22%20y%3D%2216%22%3E28%3C%2Ftext%3E%3Ctext%20font-family%3D%22math10eb3775255ffdaa027da963d8b%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2280.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22math10eb3775255ffdaa027da963d8b%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2289.5%22%20y%3D%2216%22%3E%26%23x2026%3B%3C%2Ftext%3E%3C%2Fsvg%3E)
لا.
أوجد الحدود الثلاثة التالية في كل من المتتابعات الهندسية الآتية، ثم مثل الحدود السبعة الأولى بيانياً.
8) format('truetype')%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%3C%2Fstyle%3E%3C%2Fdefs%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2213.5%22%20y%3D%2216%22%3E250%3C%2Ftext%3E%3Ctext%20font-family%3D%22math10eb3775255ffdaa027da963d8b%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2229.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2241.5%22%20y%3D%2216%22%3E50%3C%2Ftext%3E%3Ctext%20font-family%3D%22math10eb3775255ffdaa027da963d8b%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2252.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2264.5%22%20y%3D%2216%22%3E10%3C%2Ftext%3E%3Ctext%20font-family%3D%22math10eb3775255ffdaa027da963d8b%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2275.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22Arial%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2282.5%22%20y%3D%2216%22%3E2%3C%2Ftext%3E%3Ctext%20font-family%3D%22math10eb3775255ffdaa027da963d8b%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2289.5%22%20y%3D%2216%22%3E%2C%3C%2Ftext%3E%3Ctext%20font-family%3D%22math10eb3775255ffdaa027da963d8b%22%20font-size%3D%2216%22%20text-anchor%3D%22middle%22%20x%3D%2298.5%22%20y%3D%2216%22%3E%26%23x2026%3B%3C%2Ftext%3E%3C%2Fsvg%3E)
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حدد نوع المتتابعة في كل مما يأتي، هل هي حسابية، أم هندسية، أم غير ذلك. ووضح إجابتك:
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غير ذلك، لا يوجد فرق ثابت أو نسبة ثابتة.
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هندسية، الأساس
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حسابية، الأساس 4.