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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. $\newline$ $\text{–}19, \text{–}38, \text{–}57, \text{–}76, \ldots$ $\newline$ $a_n =$ _____

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Write variable expressions for arithmetic sequences

Full solution

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{–}19, \text{–}38, \text{–}57, \text{–}76, \ldots

\newline

a_n =

_____

Identify sequence type: Identify the type of sequence. $\newline$ We have: $-19$ , $-38$ , $-57$ , $-76$ , ... $\newline$ Is the given sequence geometric or arithmetic? $\newline$ $-19$ , $-38$ , $-57$ , $-76$ , ... $\newline$ 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. $\newline$ The first term, $a_1 = -19$ $\newline$ Common difference, $d = -38 - (-19) = -19$
Write nth term formula: Write the formula for the nth term of an arithmetic sequence. $\newline$ $a_n = a_1 + (n-1)d$ $\newline$ $a_1 = -19$ $\newline$ $d = -19$ $\newline$ Write an expression to describe $-19, -38, -57, -76, \ldots$ $\newline$ $a_n = a_1 + (n-1)d$ $\newline$ $a_n = -19 + (n-1)(-19)$ $\newline$ $a_n = -19 - 19n + 19$ $\newline$ $a_n = -19n$

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