Use the initial term and the recursive formula to find an explicit formula for the sequence an. Write your answer in simplest form. a1 = 3 an = an - 1 + 1 an = ______

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Use the initial term and the recursive formula to find an explicit formula for the sequence an. Write your answer in simplest form.  a1 = 3  an = an - 1 + 1    an = ______

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Given initial term and recursive formula: We are given the initial term of the sequence as a1 = 3 and the recursive formula an = an - 1 + 1. We need to determine if the sequence is arithmetic or geometric to find the explicit formula.Determining if the sequence is arithmetic or geometric: The recursive formula an = an - 1 + 1 suggests that each term is obtained by adding 1 to the previous term. This is characteristic of an arithmetic sequence, where the common difference (d) between consecutive terms is constant.Finding the common difference: To find the common difference d, we compare the recursive formula an = an - 1 + 1 with the general form of an arithmetic sequence an = a(n - 1) + d. It is clear that d = 1.Using the explicit formula for arithmetic sequence: The explicit formula for an arithmetic sequence is given by an = a1 + d(n - 1), where a1 is the first term and d is the common difference. We will use this formula to find the explicit formula for our sequence.Substituting values into the explicit formula: Substitute the given values a1 = 3 and d = 1 into the explicit formula an = a1 + d(n - 1) to get an = 3 + 1(n - 1).Simplifying the expression: Simplify the expression an = 3 + 1(n - 1) to get an = 3 + n - 1.Further simplification gives us an = n + 2. This is the explicit formula for the given sequence.

Use the initial term and the recursive formula to find an explicit formula for the sequence $a_n$ . Write your answer in simplest form. $\newline$ $a_1 = 3$ $\newline$ $a_n = a_{n - 1} + 1$ $\newline$ $a_n =$ ______

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Use the initial term and the recursive formula to find an explicit formula for the sequence ana_nan​. Write your answer in simplest form.\newlinea1=3a_1 = 3a1​=3\newlinean=an−1+1a_n = a_{n - 1} + 1an​=an−1​+1\newlinean=a_n = an​=______

Use the initial term and the recursive formula to find an explicit formula for the sequence $a_n$ . Write your answer in simplest form. $\newline$ $a_1 = 3$ $\newline$ $a_n = a_{n - 1} + 1$ $\newline$ $a_n =$ ______