Question

The sum of the first ten terms of an AP is 180 and that of the last ten is 960. If the AP has 21 terms, what is the middle term?
1. 58
2. 57
3. 56
4. Cannot be determined

Answer 1

Correct Answer - Option 2 : 57

Given: The sum of the first ten terms of an AP is 180 and that of the last ten is 960. The AP has 21 terms.

Formula used: In an AP, The middle term is equal to the average of the first and the last term.

Middle term = (a + l)/2

Sum of AP = S_n = n/2[2a + (n – 1)d] OR S_n = [(a + l)/2]n . where ‘l’ is the last term

Calculation:

Let the first term is ‘a’ and common difference is ‘d’ and the middle term is ‘x’.

According to question

Sum of first 10 terms + x + sum of last 10 terms = sum of 21 terms

⇒ 180 + x + 960 = {(a + l )/2} × 21

⇒ 1140 + x = 21x

⇒ 20x = 1140

x = 57

∴ required answer is 57