Question

in an ap if 12th term is -13, and the sum of first four term is 24. what is the sum of the first 10 terms. ( use formula)

Answer 1

t12=-13 t12= a+(12-1)d ------->a+11d=-13 -------->a=-13-11d........(i)
s4=4/2(2a+(n-1)d)
24=2(2a+3d)
24/2=2(-13-11d)+3d ( from (i))
12=-26-22d+3d
12+26=-19d
38/19=-d
-2=d
putting value of d on eq (i)
a=-13-11d
a=-13-11×-2
a=-13+22
a= 9
s10 =10/2(2×9+(10-1)×-2)
=5(18+9×-2)
=5(18-18)
= 5×0
s10=0
I hope it will help you!!!!

Answer 2

T12 = - 13
a + 11d = -13
a = -13 - 11d.......( i )

T1 + T2 + T3 + T4 = 24
a + (a+d) + (a+2d) + (a+3d) = 24
4a + 6d = 24
4 (-13 - 11d ) + 6d = 24
-52 - 44d+ 6d = 24
-52 - 38d = 24
38 d = - 76
d = -2
from eq (i)
a = -13 - 11 x (-2)
a = -13 + 22
a = 9
Sn = n/2 { 2a + (n-1)d }
S10 = 10/2 (2 x 9 + 9 x -2 )
S10 = 5 ( 18 -18 )
S10 = 5 x 0
S10 = 0
Hope this will helpful 4 u...
Rahul