An AP 8, 10, 12, ... has 60 terms. Find its last term. Hence, find the sum of its last 10 terms.
Here, First term = a = 8
Common difference = d = 10 - 8 = 2
No. of terms = 60
∴ last term will be 60th term.
Using the formula for finding nth term of an A.P.,
l = a60 = a + (60 - 1) × d
∴ l = 8 + (60 - 1) × 2
⇒ l = 8 + 118 = 126
Now, sum of last 10 terms = sum of first 60 terms - sum of first 50 terms
i.e. sum of last 10 terms = S60 - S50
Now, Sum of first n terms of an AP is
Sn = [2a + (n - 1)d]
∴ Sum of first 50 terms is given by:
S50 = [2(8) + (50 - 1)(2)]
= 25 × [16 + 98]
= 25 × 114
= 2850
Now, Sum of first 60 terms is given by:
S60 = [2(8) + (60 - 1)(2)]
= 30 × [16 + 118]
= 30 × 248
= 4020
Now, S60 - S50 = 4020 - 2850
= 1170
∴ last term = 126, sum of last 10 terms = 1170