Answer :
Final answer:
The explicit formula for the sequence 13, 65, 325, 1625, 8125 is given by a_n = 13 × 5^{n-1}. This is determined by recognizing that each term in the sequence is five times the previous term.
Explanation:
When looking at the sequence 13, 65, 325, 1625, 8125 and trying to find an explicit formula, it is important to recognize the pattern. Each term is five times the previous term. This allows us to derive the formula for the nth term of the sequence, which is given by multiplying the first term by 5 raised to the power of n-1 (since the first term corresponds to n=1).
The explicit formula for this sequence is a_n = 13 × 5^{n-1}.
To illustrate this with an example, the second term when n=2 would be 13 × 5^{2-1} = 13 × 5 = 65, which matches the sequence provided.
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