Question

How many terms for ap:9,17,25..to make sum 636?

Answer 1

GIVEN

A. P is 9, 17, 25,...
First term 'a' = 9
Second term 'a2' = 17
Common difference 'd'
= 2nd term - first term
= 17 - 9
= 8
SUM 'Sn' = 636

FIND NUMBER OF TERMS 'n' = ?

FORMULA for SUM of A. P is
Sn = n / 2 [2a + (n - 1) d]

SUBSITUTE THE GIVEN VALUES in Sn
636 = n / 2 [ (2 x 9) + (n - 1) 8]
636 = [ n (18 + 8n - 8)] / 2

CROSS MULTIPLY
636 x 2 = 18n + 8n^2 - 8n
1272 = 10n + 8n^2
8n^2 + 10n - 1272 = 0 ............... (1)

DIVIDE by 2 as all terms are multiple of 2 in (1)
4n^2 + 5n - 636 = 0

FACTORIZE 4n^2 + 5n - 636 = 0
= 4n^2 + 53n - 48n - 636 = 0
= n (4n + 53) - 12 (4n + 53) = 0
(4n + 53) (n - 12) = 0
(4n + 53) = 0 & (n - 12) = 0
n = - 53 / 4 & n = 12
**As number of terms cannot be in negative and in fraction. Therefore, eliminate n = - 53 / 4

NUMBER OF TERMS is 12

Answer 2

Step-by-step explanation:

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