The sum of 2n terms of A.P. {1, 5, 9, 13…..} is greater than sum of n terms of…
20242023202420242024
The sum of 2n terms of A.P. {1, 5, 9, 13…..} is greater than sum of n terms of A.P. = {56, 58, 60..…}. What is the smallest value n can take?
- A.
9
- B.
10
- C.
12
- D.
14
Attempted by 22 students.
Show answer & explanation
Correct answer: A
First AP: a=1, d=4. Sum of 2n terms = n(8n-2) = 8n^2 - 2n.
Second AP: a=56, d=2. Sum of n terms = n(n+55) = n^2 + 55n.
Inequality: 8n^2 - 2n > n^2 + 55n simplifies to 7n^2 - 57n > 0.
Since n>0, 7n > 57 => n > 8.14.
Smallest integer n = 9.