Question

In A.P if the 12th term is -13 and the sum of its first four terms is 24 find the sum of its first 10 terms

Answer 1

A12 = a + ( 12 - 1) d

-13 = a + 11d

a = - 13 - 11d

S4 = 24

4/2[ 2a + 3d ] = 24

2( 2a +3d) = 24

4a + 6d = 24

4( - 13 - 11d) + 6d = 24

- 52 - 44d + 6d = 24

- 38d = 24 +52 = 76

d = - 76/38 = - 2

Common difference, d = - 2

a = - 13 - 11d

a = - 13 - 11( - 2)

a = - 13 + 22 = 9

First term, a = 9

S10 = 10/2 [ 2× 9 + ( 10 - 1) ( - 2)]

S10 = 5( 18 - 18)

$\fbox{S10\: =\: 0}$