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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. $\newline$ $\text{–}39, \text{–}78, \text{–}117, \text{–}156, \ldots$ $\newline$ $a_n =$ _____

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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

\text{–}39, \text{–}78, \text{–}117, \text{–}156, \ldots

\newline

a_n =

_____

Identify sequence type: Identify the type of sequence. $\newline$ We have: $-39$ , $-78$ , $-117$ , $-156$ , ... $\newline$ Is the given sequence geometric or arithmetic? $\newline$ $-39$ , $-78$ , $-117$ , $-156$ , ... $\newline$ Here, there is a common difference between consecutive terms. $\newline$ The given sequence is arithmetic.
Determine values of $a_1$ and $d$ : Determine the values of $a_1$ and $d$ of the sequence. The first term, $a_1 = -39$ Common difference, $d = -78 - (-39) = -39$
Write nth term formula: Write the formula for the nth term of an arithmetic sequence. $\newline$ $a_n = a_1 + (n-1)d$ $\newline$ $a_1 = -39$ $\newline$ $d = -39$ $\newline$ Write an expression to describe $-39, -78, -117, -156, ...$ $\newline$ $a_n = a_1 + (n-1)d$ $\newline$ $a_n = -39 + (n-1)(-39)$
Simplify expression: Simplify the expression. $\newline$ $a_{n} = -39 + (-39n + 39)$ $\newline$ $a_{n} = -39n + 39 - 39$ $\newline$ $a_{n} = -39n$

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