# How many terms of the A.P 9, 17, 25... must be added together to get 636 as the sum

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Given: a = 9 & d= 17-9 = 8 sum= 636

the formula to find the Sum of AP

Sn = n/2(2a + (n-1)d)

636 = n/2(2*9 + (n-1) 8)

636 * 2 = n( 18 + 8n - 8)

1272 = n( 10 + 8n)

10n + 8n^2 = 1272

8n^2 +10n - 1272 =0

for finding n formula = -b

-------------------------

2a

n = [ -10

= [-10

= [-10

= (-10

= (-10+202)/16 & (-10-202)/16

= 12 & -13.25

-13.25 does not exist

So n=12 is the solution