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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. $\newline$ $40, 80, 120, 160, \ldots$ $\newline$ $a_n =$ _____

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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

40, 80, 120, 160, \ldots

\newline

a_n =

_____

Sequence Type: We have: $\newline$ $40, 80, 120, 160, \ldots$ $\newline$ Is the given sequence geometric or arithmetic? $\newline$ $40, 80, 120, 160, \ldots$ $\newline$ Here, there is a common difference between consecutive terms. $\newline$ The given sequence is arithmetic.
Find $a_1$ and $d$ : Determine the values of $a_1$ and $d$ of the sequence. $\newline$ The first term, $a_1 = 40$ $\newline$ Common difference, $d = 80 - 40 = 40$
Expression for Sequence: We have: $\newline$ $a_n = a_1 + (n-1)d$ $\newline$ $a_1 = 40$ $\newline$ $d = 40$ $\newline$ Write an expression to describe $40$ , $80$ , $120$ , $160$ , ... $\newline$ $a_n = a_1 + (n-1)d$ $\newline$ $a_n = 40 + (n-1) \times 40$ $\newline$ $a_n = 40 + 40n - 40$ $\newline$ $a_n = 40n$

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