# Find the number of terms of the A.P. 25,22,19,... are needed to give the sum 116? Also find the last term.

Sir please give me the detailed solution of this question as it is very for examination

ML Aggarwal

Arithmetic Progression

Chapter 9

Question no 7(i)

Here a=25,d=−3,Sn=116

we know

Sn=2n[2a+(n−1)d]

116=2n[2×25+(n−1)(−3)]

⇒232=n(50−3n+3)

⇒232=n(53−3n)

⇒232=53n−3n2

⇒3n2−53n+232=0

⇒3n2−24n−29n+232=0

⇒3n(n−8)−29(n−8)=0

⇒(3n−29)(n−8)=0

∴n=8,n=329 (fraction)

∴ Number of terms required = ‘8’

tn=a+(n−1)d

⇒tn=25−1(8−1)(−3)

⇒tn=25−21=4

Hence, Last term is ‘4’