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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. $\newline$ $84, 168, 252, 336, \ldots$ $\newline$ $a_n =$ _____

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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

84, 168, 252, 336, \ldots

\newline

a_n =

_____

Given Sequence Analysis: We have: $\newline$ $84, 168, 252, 336, \ldots$ $\newline$ Is the given sequence geometric or arithmetic? $\newline$ To determine this, we can look at the differences or ratios between terms.
Calculate Constant Difference: Calculate the difference between consecutive terms to see if it is constant: $168 - 84 = 84$ $252 - 168 = 84$ $336 - 252 = 84$ Since the difference is constant, the sequence is arithmetic.
Find $a_1$ and $d$ : Determine the values of $a_1$ and $d$ for the sequence. $\newline$ The first term, $a_1 = 84$ $\newline$ Common difference, $d = 168 - 84 = 84$
Arithmetic Sequence Formula: Write the formula for the nth term of an arithmetic sequence: $\newline$ $a_n = a_1 + (n-1)d$ $\newline$ Substitute the values of $a_1$ and $d$ into the formula: $\newline$ $a_n = 84 + (n-1)\times84$
Simplify Expression: Simplify the expression: $\newline$ $a_{n} = 84 + 84n - 84$ $\newline$ $a_{n} = 84n$

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