Question

How many term of ap 63, 60, 57 must be taken so that sum is 693?

Answer 1

Answer:

636750 is your answer.

Answer 2

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here is your answer:

let a be the fist term and d be the common difference

first term = a = 63

common difference = d = a2-a1 = -3

also given that sum of the terms = 693

n/2[2a+(n-1)d] = 693

n/2[2*63+(n-1)-3 = 693

n/2[126-3n+3] = 693

n/2[129-3n] = 693

n*3[43-n] = 693*2

n[43-n] = 1386/3

43n-n^2 = 462

43n-n^2-462 = 0

Xing -1

n^2-43n+462 = 0

n^2-22n-21n+462 = 0

n(n-22)-21(n-22) = 0

(n-22)(n-21) = 0

n-22 = 0 (or) n-21 = 0

n = 22 (or) n = 21

hence required number of terms is 21 or 22

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