Question

If an A.p if the 12th term is -13 and the sum of first four term is 24 what is the sum of first 10 term

Answer 1

Let the first term be a and the common difference be 'd'.
Then 12th term =a+(12-1)d
= a+11d.
A.T.Q,
a+11d=-13
Also
The sum of first four terms is 24.
hence
24=(n÷2){2a+(n-1)d}
24=2(2a+3d)
24=4a+6d
12=2a+3d

(a+11d=-13)×2
2a+3d=12

2a+22d=-26
2a+ 3d = 12
__________
19d=-38
d = -2

a+(-22)=-13
a = 22-13
= 9
now,
Sum of first 10 terms = =5{2×9 + (10-1)(-2)}
=5{18+(-18)}
=5{0}
=0.