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In an arithmetic progression it is given that a=2, d=8, Sn=90. Find n and an.

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answer is B.

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Detailed Solution

S_{n} = \frac{n}{2} [2 a + (n - 1) d]

90 = \frac{n}{2} [2 (2) + (n - 1) 8]

180 = n [4 + 8 n - 8]

180 = 8 n^{2} - 4 n

2 n^{2} - n - 45 = 0

2 n^{2} - 10 n + 9 n - 45 = 0

2 n (n - 5) + 9 (n - 5) = 0

(n - 5) (2 n + 9) = 0

n = 5 or n = - \frac{9}{2}

Since n cannot be negative hence n = 5

a_{n} = a + (n - 1) d

a_{n} = 2 + (5 - 1) 8

a_{n} = 2 + 32 = 34

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