UPSC NDA Math Model Paper 6

Given: The sequence is 25, 22, 19,...... and the sum of certain number of terms of this sequence is 115
Let there n be term of the given sequence such that Sn=115
Here, a = 25, d = - 3
As we know that, Sn=

n

2

×[2a+(n−1)d]
⇒Sn=

n

2

×[2.(25)+(n−1)(−3)]=115
⇒3n2−53n+230=0
⇒n=10 or 23∕3 but ∵n is natural number
⇒n=10
As we know that,Sn=

n

2

×[a+l] where 1 is the last term.
⇒S10=

10

2

×[25+l]=115
⇒l=−2
Hence, the last term is - 2