అంకశ్రేఢులు (Arithmetic Progressions) · Practice MCQs

Correct: C — 10

a = 23, d = −2, aₙ = 5 → 5 = 23 + (n − 1)(−2) → n − 1 = 9 → n = 10.

Correct: D — -979

a = 8, d = −5, n = 22: S = 22/2 [16 + 21(−5)] = 11 × (16 − 105) = 11 × (−89) = −979.

Correct: A — 1046.5

d = 3.5, n = (84 − 7)/3.5 + 1 = 23. S = 23/2 (7 + 84) = 23 × 91/2 = 1046.5.

Correct: B — 200

1050 = 14/2 [20 + 13d] = 140 + 91d → 910 = 91d → d = 10. a₂₀ = 10 + 19×10 = 200.

Correct: C — 12

n/2 [18 + 8(n − 1)] = n(4n + 5) = 636 → 4n² + 5n − 636 = 0 → n = 12. (S₁₂ = 6 × (18 + 88) = 636.)

Correct: D — 8/3

S = n/2 (a + l) → 400 = n/2 × 50 → n = 16. l = a + 15d → 45 = 5 + 15d → d = 40/15 = 8/3.

Correct: A — 100

a + 3d = 7 (S₇ = 7(a + 3d)), a + 8d = 17 (S₁₇ = 17(a + 8d)) → d = 2, a = 1. Sₙ = n/2 [2 + 2(n−1)] = n² → S₁₀ = 100.

Correct: B — 4920

a = 6, d = 6, n = 40: S = 20 × (12 + 39×6) = 20 × 246 = 4920. (లేదా 6 × 40×41/2 = 6 × 820.)

Correct: C — 625

బేసి సంఖ్యలు 1, 3, …, 49 → n = 25. S = n² = 625. (లేదా 25/2 × (1 + 49) = 625.)

Correct: D — -15

S₁₀ = 40 − 100 = −60, S₉ = 36 − 81 = −45. a₁₀ = S₁₀ − S₉ = −60 + 45 = −15. (aₙ = 5 − 2n → a₁₀ = −15.)