Question

An AP 5, 12, 19, .... has 50 term. Find its last term. Hence, find the sum of its last 15 terms.

Answer 1

The given AP is 5,12,19,.......
Here, a = 5,d =12- 5 = 7 and n = 50.
Since there are 50 terms in the AP, so the last term of the AP is  a₅₀.

l= a ₅₀ = 5 +(50-1) × 7                     [ a_n= a + (n-1) d]

= 5 +343

=348

Thus, the last term of the AP is 348.
Now,
Sum of the last 15 terms of the AP

= S₅₀  - S₃₅ 

`= 50/2 [2 xx 5 +(50-1) xx 7 ] - 35/2 [ 2 xx 5 + (35-1) xx 7 ]`

`{S_n = n/2 [ 2a + (n-1) d]}`

`= 50/2 xx (10+343 ) - 35/2 xx (10+ 238)`

`= 50/2 xx 353 - 35/2 xx 248`

`=(17650 - 8680)/2`

`=8970/2`

= 4485

Hence, the require sum is 4485.