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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. $\newline$ $99, 100, 101, 102, \ldots$ $\newline$ $a_n =$ _____

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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

99, 100, 101, 102, \ldots

\newline

a_n =

_____

Sequence Type: We have the sequence: $99, 100, 101, 102, ext{...}$ $\newline$ Is the given sequence geometric or arithmetic? $\newline$ $99, 100, 101, 102, ext{...}$ $\newline$ 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, $a_1 = 99$ $\newline$ Common difference, $d = 100 - 99 = 1$
Arithmetic Sequence Formula: We have the formula for the nth term of an arithmetic sequence: $\newline$ $a_n = a_1 + (n-1)d$ $\newline$ $a_1 = 99$ $\newline$ $d = 1$ $\newline$ Write an expression to describe $99$ , $100$ , $101$ , $102$ , ... $\newline$ $a_n = 99 + (n-1) \times 1$ $\newline$ $a_n = 99 + n - 1$ $\newline$ $a_n = n + 98$

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