Question

find the 60th term of the AP 8,10,12,if it has a total of 60 terms and hence find the sum of its last ten terms?

Answer 1

A.P. 8 , 10 , 12, ...

First term = a = 8

Common difference = d = 10 - 8 = 12 - 10 = 2

Formula of nth term of A.P Tn = a + ( n - 1 ) d

Using formula

60th term of given A.P.

T60 = 8 + ( 60 - 1 ) 2 = 8 + 59 × 2 = 8 + 118 = 126

Sum of first n terms of an AP =
Sn = n2[2a+(n−1)d]
Using formula
S60 = 602[2×8+(60−1)×2]
= 4020
Similarly
S50 = 502[2×8+(50−1)×2]
= 2850

Sum of last 10 terms
= S60 − S50
= 4020 – 2850
= 1170

Answer 2

As given AP is 8,10,12,........
so a1=8
d=a2-a1=10-8=2
n=60
to find 60th term a60
a60=a1+(n-1)d
a60=8+(60-1)2=126
Sum of terms
Sn=n2[2a1+(n-1)d]
S60=60.2[2.8+(60-1)2]
S60=4020
To find
S50=50.2[2.8+(50-1)2]
S50=2850
Sum of last 10 terms=S60-S50=4020-2850=1170