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 = Sn = n/2[2a + (n – 1)d] OR Sn = [(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