Question

the 7th term of an A.P. is -4 and its 13th term is -16. find the sum of its first 19 terms

Answer 1

T7=-4 = a +6d
T13=-16 = a+12d
Subtracting....
A+12d=-16 - (a+6d =-4) =6d=-12 so d=-2.....
Now a=-4-6(-2)=4+12=16
S19=19/2(2(16)+18(-2)) = 19(16-18) =19(-2) =-38...
I hope its helpful.....

Answer 2

a+6d = -4 1
a+12d=-16. 2
6d= -12
d= -2
put value of d in 1 a+ 6×-2
a-12 = -4
a =12-4
a = 8
a19= a+ 18d =
8+18×-2
8-36
a19= -28