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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. $\newline$ $–32, –31, –30, –29, \ldots$ $\newline$ $a_n =$ _____

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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

–32, –31, –30, –29, \ldots

\newline

a_n =

_____

Sequence Type: We have: $\newline$ – $32$ , – $31$ , – $30$ , – $29$ , ... $\newline$ Is the given sequence geometric or arithmetic? $\newline$ – $32$ , – $31$ , – $30$ , – $29$ , ... $\newline$ Here, there is a common difference between consecutive terms. $\newline$ The given sequence is arithmetic.
Values Determination: Determine the values of $a_1$ and $d$ of the sequence. $\newline$ The first term, $a_1 = -32$ $\newline$ Common difference, $d = -31 - (-32) = 1$
Expression Writing: We have: $\newline$ $a_n = a_1 + (n-1)d$ $\newline$ $a_1 = -32$ $\newline$ $d = 1$ $\newline$ Write an expression to describe $-32, -31, -30, -29, ...$ $\newline$ $a_n = a_1 + (n-1)d$ $\newline$ $a_n = -32 + (n-1) \times 1$ $\newline$ $a_n = -32 + n - 1$ $\newline$ $a_n = n - 33$

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