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The first and the last terms of an AP are 5 and 45 respectively. If the sum of all its terms is 400, then what is the common difference?

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d = 89

d = 85

d = 83

d = 87

answer is B.

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Detailed Solution

Given:

a = 5, l = 45 and S n = 400

.
Let there are n terms in the A.P.
Formula used for sum of first term of A.P.:

S n = n 2 [a + l]

Applying sum of n terms of an A.P. formula:

∴ S n = 400 ⇒ n 2 (5 + 45) = 400 ⇒ n 2 × 50 = 400 ⇒ n = 400 × 2 50

⇒ n = 16
Thus, there are 16 terms in the A.P.
Let d be the common difference of the A.P.
Formula for the

n t h

term:

a n = a + n − 1 × d

Applying nth term of an A.P. formula:

∴ a 16 = 45 5 + (16 − 1) × d = 45 ⇒ 15 d = 45 − 5 ⇒ 15 d = 40

⇒ d = 4015 ⇒ d = 83

Therefore, the common difference of the A.P. is

83

.
Hence, option (2) is correct.

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