Multiple choice

How many terms of the series 8, 12, 16 … must be taken, so that they add up to 476?

  1. 9

  2. 12

  3. 14

  4. 18

  5. 23
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C Correct answer
Explanation

This is an arithmetic progression with first term a=8 and common difference d=4. The sum formula is S = n/2 * (2a + (n-1)d), so 476 = n/2 * (16 + (n-1)4). Solving 476 = 2n^2 + 6n leads to n^2 + 3n - 238 = 0, which factors to (n+17)(n-14) = 0, giving n=14.

AI explanation

The given sequence is an arithmetic progression where the first term a is 8 and the common difference d is 4. Using the sum formula Sn = n/2 * (2a + (n - 1)d), we set the equation to 476 = n/2 * (16 + (n - 1)4). Simplifying the expression inside the parentheses gives 12 + 4n, so we have n * (12 + 4n) = 952. Solving the quadratic equation 4n^2 + 12n - 952 = 0 gives n = 14.

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