how many terms of a.p. 9,17,25.. are required to get sum of 450?

Asked by Gayatri Narkhede | 1st Dec, 2013, 12:45: PM

Expert Answer:

The AP is 9, 17, 25,.......

a (first term) = 9

d (common difference) = 17-9 = 8

Let n be the required number of terms.

Sn (sum of the n terms) = 450

We know that Sn = n/2 (2a + (n-1)d )

450 = n/2 (18 + (n-1)8 )

900 = n(18 + 8n -8)

900 = 8n2 + 10n

8n2 + 10n -900 = 0

8n2 +80n -90n -900 = 0 

8n (n +10) -90 (n- 10) = 0

(n-10)(8n-90) = 0

n = 10 or 11.25

But n has to be a natural, since number of terms is always a natural number.

Thus, the required number of terms is 10.

Answered by  | 1st Dec, 2013, 02:39: PM

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