Multiple choice

The nth term of the following given sequence is 301. Find the value of n. 4, 7, 11, 16, ...

  1. 20

  2. 21

  3. 22

  4. 23
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D Correct answer
Explanation

The sequence is 4, 7, 11, 16. The differences are 3, 4, 5. This is a quadratic sequence where the nth term is given by n^2/2 + 3n/2 + 2. Setting this equal to 301, n^2 + 3n - 598 = 0. Solving for n using the quadratic formula gives n=23.

AI explanation

This is an arithmetic progression with a first term of 4 and a second term of 7, giving a common difference of 3. The formula for the nth term is a + (n - 1)d, so we set 301 = 4 + (n - 1)3. Solving this equation, 297 = (n - 1)3, which simplifies to n - 1 = 99. Therefore, the value of n is 23.

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