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Question: Write a recursive formula for the sequence 4, 9, 14, 19, 24, ... Then find the next term.
A recursive formula for a sequence is a formula that relates each term with the ones before it. For the given sequence 4, 9, 14, 19, 24, ..., the difference between any two consecutive terms is 5. Thus, we can write a recursive formula for this sequence in the following way: a₁ = 4 (The first term is 4) aₙ = aₙ₋₁ + 5 This formula means that to get any term in the sequence (aₙ), you take the previous term (aₙ₋₁) and add 5. To find the next term after 24, we simply add 5 (since the difference is constant and equals 5), so the next term would be 24 + 5 = 29.
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