Question

if the sum of n terms of a series be 5n^2+3n find n term of this series in AP
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Answer 1

Step-by-step explanation:

Sn = 5n^2 +3n

if n = 1 then

S1 = 5(1)^2 + 3*1 = 8

put n = 2

S2 = 5(2)^2 + 3*2 = 26

put n = 3

S3 = 5(3) ^2 + 3*3 = 54

now

A1 = S1 = 8

A2 = S2 - S1 = 26-8 = 18

A3 = S3 -S2 = 54-26 = 28

here a= 8

d = 18-8 = 10

An = a+ (n-1)*d

= 8+ ( n-1) *10

= 8+ 10n -10

= 10n -2