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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. 


Solution

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 ........
 

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