What is the next number in the sequence: 4, 11, 25, 53, ...?

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Multiple Choice

What is the next number in the sequence: 4, 11, 25, 53, ...?

Explanation:
A pattern here is that the increases between terms double each time. From 4 to 11 is +7, from 11 to 25 is +14, and from 25 to 53 is +28. Each increment doubles, so the next increase should be 56. Adding that to 53 gives 109. You can also see it with a formula: a_n = 4 + 7(2^{n-1} - 1); for the next term, n = 5, you get 4 + 7(16 - 1) = 109. So the next number is 109.

A pattern here is that the increases between terms double each time. From 4 to 11 is +7, from 11 to 25 is +14, and from 25 to 53 is +28. Each increment doubles, so the next increase should be 56. Adding that to 53 gives 109. You can also see it with a formula: a_n = 4 + 7(2^{n-1} - 1); for the next term, n = 5, you get 4 + 7(16 - 1) = 109. So the next number is 109.

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