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Write an expression to describe the sequence below. Use $n$ to represent the position of a term in the sequence, where $n = 1$ for the first term. $\newline$ $59, 118, 177, 236, \ldots$ $\newline$ $a_n =$ _____

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Write variable expressions for arithmetic sequences

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Q. Write an expression to describe the sequence below. Use

n

to represent the position of a term in the sequence, where

n = 1

for the first term.

\newline

59, 118, 177, 236, \ldots

\newline

a_n =

_____

Sequence Type: We have the sequence: $59, 118, 177, 236, \ldots$ $\newline$ Is the given sequence geometric or arithmetic? $\newline$ $59, 118, 177, 236, \ldots$ $\newline$ Here, there is a common difference between consecutive terms. $\newline$ The given sequence is arithmetic.
Initial Values: Determine the values of $a_1$ and $d$ of the sequence. $\newline$ The first term, $a_1 = 59$ $\newline$ Common difference, $d = 118 - 59 = 59$
Arithmetic Sequence Formula: We have the formula for the $n$ th term of an arithmetic sequence: $a_n = a_1 + (n-1)d$ $a_1 = 59$ $d = 59$ Write an expression to describe the sequence $59$ , $118$ , $177$ , $236$ , ... $a_n = 59 + (n-1) \times 59$
Simplify Expression: Simplify the expression: $\newline$ $a_{n} = 59 + 59n - 59$ $\newline$ $a_{n} = 59n$

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