Question

An AP 8, 10, 12, ... has 60 terms. Find its last term. Hence, find the sum of its last 10 terms.

Answer 1

The given AP is 8, 10, 12,......

Here, a = 8, d = 10 – 8 = 2 and n = 60

Since there are 60 terms in the AP, so the last term of the AP is a₆₀.

l = a₆₀ = 8 + (60 – 1) × 2   ...[a_n = a + (n – 1)d]  

= 8 + 118

= 126

Thus, the last term of the AP is 126.

Now,

Sum of the last 10 terms of the AP

= S₆₀ – S₅₀ 

= `60/2 [2 xx 8 + (60 - 1) xx 2] - 50/2 [2 xx 8 + (50 - 1) xx 2]`   ...`{S_n = n/2 [2a + (n - 1)d]}`

= 30 × (16 + 118) – 25 × (16 + 98) 

= 30 × 134 – 25 × 114

= 4020 – 2850

= 1170

Hence, the required sum is 1170.