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Use the initial term and the recursive formula to find an explicit formula for the sequence $a$ . Write your answer in simplest form. $\newline$ $a = -49$ $\newline$ $a = a - 16$ $\newline$ $a =$ ______

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Convert a recursive formula to an explicit formula

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Q. Use the initial term and the recursive formula to find an explicit formula for the sequence

a

. Write your answer in simplest form.

\newline

a = -49

\newline

a = a - 16

\newline

a =

______

Given Sequence Type: We have: $\newline$ Initial term $a_1 = -49$ $\newline$ Recursive formula: $a_n = a_{n-1} - 16$ $\newline$ Is the given sequence geometric or arithmetic? $\newline$ The recursive formula $a_n = a_{n-1} - 16$ corresponds to $a_n = a_{n - 1} + d$ . $\newline$ Hence, the given sequence is arithmetic.
Common Difference: Recursive formula: $a_n = a_{n-1} - 16$ Find the common difference in the arithmetic sequence. Compare $a_n = a_{n-1} - 16$ with $a_n = a_{n - 1} + d$ to find $d$ . So, $d = -16$ .
Explicit Formula: Explicit formula for arithmetic sequence: $\newline$ $a_n = a_1 + d(n - 1)$ $\newline$ Here, $a_1$ is the first term, and $d$ is the common difference. We have: $\newline$ $a_1 = -49$ $\newline$ $d = -16$ $\newline$ Find the explicit formula. $\newline$ Substitute $-49$ for $a_1$ and $-16$ for $d$ in $a_n = a_1 + d(n - 1)$ . $\newline$ $a_1$ $0$ $\newline$ $a_1$ $1$ $\newline$ $a_1$ $2$ $\newline$ $a_1$ $3$ $\newline$ Explicit formula is: $a_1$ $4$

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