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) xx2 ] - 50/2 [ 2xx 8 + (50-1) xx2]`

`{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.