Question

Find the sum of last ten terms of the A.P.: 8, 10, 12, 14, .., 126.

Answer 1

Given: AP: 8, 10, 12, 14, .., 126. We need the sum of the last 10 terms.

Step-wise calculation:

1. Write the last 10 terms in reverse so the first term of that 10-term block is 126.

Then a = 126 and the common difference for the reversed list is d = 124 – 126 = –2.

2. Use the sum formula `S_n = n/2 [2a + (n - 1)d]` with n = 10:

`S_10 = 10/2 [2(126) + (10 - 1)(-2)]`

S₁₀ = 5[252 + 9(–2)] 

= 5[252 – 18]

= 5 × 234

= 1170

The sum of the last ten terms of the A.P. is 1170.