Question

If the nth term of an AP is 7-3n, find the sum of twenty five terms

Answer 1

Assuming nth term of the AP as 1st term of the same AP.

nth term = 7 - 3n

1st term = 7 - 3( 1 )

a = 7 - 3

a = 4

Assuming nth term of the AP as last term ( 25th ) of the same AP.

nth term = 7 - 3n

25th term = 7 - 3( 25 )

l = 7 - 75

l = - 68

We know, $S_{n} = \dfrac{n}{2}[a+l]$

Therefore,

$S_{25} = \dfrac{25}{2}[4+(-68)$

$S_{25} = \dfrac{25}{2}[4-68]$

$S_{25} = \dfrac{25}{2}[-66]$

$S_{25} = 25( - 33 )$

$S_{25} =-825$

Therefore, sum of 25 terms is -825.