Question

In an AP the sum of the first 10 terms is -150 and the sum of its next 10 terms is -550.find the AP.

Answer 1

Let a is the first term and d is the common difference of AP
now use formula,
Sn=n/2{2a+(n-1) d}

now
S10=10/2 {2a+(10-1) d}
-150=5 (2a+9d)
2a+9d =-30--------------(1)

again
S20-S10=-550

20/2 {2a+19d} +150=-550

10 (2a+19d)=-11/3

2a+19d=-11/30-----------------(2)

solve both equation
d=-79/300
a=89/600