Question

In an A.P., the sum of first ten terms is -150 and the sum of its next ten terms is -550 Find the A.P.

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=-280

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

10 (2a+19d)=-700

2a+19d=-70 -----------------(2)

solve both equation
10d=-40
d=-4

a=3

hence 3,-1,-5.-9 ........