Arithmetic and Geometric Progression
ICSE · Class 10 · Mathematics
Most important questions from Arithmetic and Geometric Progression for ICSE Class 10 Mathematics board exam 2026. MCQs, short answer, and long answer questions with marks.
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Which of the following sequences are arithmetic progressions?
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2, 5, 8, 11, 14, 10, 7, 4, 1, -2, 15, 15, 15, 15, 15
AP has constant difference. (1) d=3, (2) squares-not AP, (3) d=-3, (4) GP with r=2, (5) d=0. Options 1, 3, and 5 are APs.
If the sum of first n terms of an AP is 3n² + 2n, find the common difference.
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6
Given Sn = 3n² + 2n. T1 = S1 = 3(1)² + 2(1) = 5. T2 = S2 - S1 = [3(4) + 4] - 5 = 16 - 5 = 11. d = T2 - T1 = 11 - 5 = 6.
Three numbers in GP have sum 14 and product 64. Find the middle term.
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4
Let numbers be a/r, a, ar. Sum: a/r + a + ar = 14. Product: (a/r) × a × ar = a³ = 64, so a = 4. The middle term is 4.
Find the number of terms in the AP: 7, 13, 19, ..., 205
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34
a = 7, d = 6, last term l = 205. Using l = a + (n-1)d: 205 = 7 + (n-1)6. Solving: 198 = (n-1)6, so n-1 = 33, therefore n = 34.
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