Question

The 12th term of a.p. is -13 and sum of first four terms is 24, find sum of first 10 terms.

Answer 1

Answer:

let the 1st term is a

and common difference is d

then, 12 th term =a+(12-1).d= -13

=> a+11d= -13

=> a= -13-11d

again,

sum of 1st four terms=24

4/2{2a+(4-1).d}=24

=> 2{2a+3d}=24

=> 2a+3d=24/2

=> 2a+3d=12

putting the value of a

2(-13-11d)+3d=12

=> -26-22d+3d=12

=> -19d=12+26

=> -19d=38

=> d= 38/-19

=> d= -2

a= -13-11d= -13-11(-2)= -13+22=9

sum of 1st 10 terms

=10/2{2a+(10-1).d}

=5{2.9+9.(-2)}

=5(18-18)

=5.0

=0

so, sum of the 1st 10 terms is 0