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Find a formula for s^n, n ≥ 1, for the sequence -1, 2, 7, 14, 23...

User Daniza
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Final answer:

The formula for s^n in the sequence -1, 2, 7, 14, 23... is sⁿ = 2n².

Step-by-step explanation:

The sequence -1, 2, 7, 14, 23... can be represented by the formula sⁿ = 2n².

To find this formula, we notice that the difference between consecutive terms increases by 5 each time. Taking the difference between consecutive terms gives us 3, 5, 7, 9... which is the sequence of odd numbers. We can express this sequence as (2n - 1), where n starts from 1.

Multiplying the sequence (2n - 1) by 2 gives us the formula sⁿ = 2(2n - 1) = 2(2n - 2 + 1) = 4n - 2 + 2 = 4n. Simplifying further, we get sⁿ = 2n².

User Kenarsuleyman
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