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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. $\newline$ $42, 84, 126, 168, \ldots$ $\newline$ $a_n =$ _____

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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

42, 84, 126, 168, \ldots

\newline

a_n =

_____

Sequence Type: We have: $\newline$ $42, 84, 126, 168, \ldots$ $\newline$ Is the given sequence geometric or arithmetic? $\newline$ $42, 84, 126, 168, \ldots$ $\newline$ Here, there is a common difference between consecutive terms. $\newline$ The given sequence is arithmetic.
Find $a_1$ and $d$ : $42, 84, 126, 168, \dots$ $\newline$ Determine the values of $a_{1}$ and $d$ of the sequence. $\newline$ The first term, $a_{1} = 42$ $\newline$ Common difference, $d = 84 - 42 = 42$
Expression for Sequence: We have: $\newline$ $a_n = a_1 + (n-1)d$ $\newline$ $a_1 = 42$ $\newline$ $d = 42$ $\newline$ Write an expression to describe $42$ , $84$ , $126$ , $168$ , ... $\newline$ $a_n = a_1 + (n-1)d$ $\newline$ $a_n = 42 + (n-1) \times 42$ $\newline$ $a_n = 42 + 42n - 42$ $\newline$ $a_n = 42n$

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