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’