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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. $\newline$ $80, 81, 82, 83, \ldots$ $\newline$ $a_n =$ _____

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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

80, 81, 82, 83, \ldots

\newline

a_n =

_____

Identify sequence type: Identify the type of sequence. $\newline$ The sequence is $80, 81, 82, 83, \ldots$ $\newline$ We notice that there is a constant difference between consecutive terms, which means the sequence is arithmetic.
Determine first term and difference: Determine the first term ( $a_1$ ) and the common difference ( $d$ ) of the sequence. $\newline$ The first term, $a_1$ , is $80$ . $\newline$ The common difference, $d$ , is the difference between any two consecutive terms, which is $81 - 80 = 1$ .
Write general nth term formula: Write the general formula for the nth term of an arithmetic sequence. $\newline$ The nth term of an arithmetic sequence is given by the formula: $\newline$ $a_n = a_1 + (n-1)d$
Substitute values into formula: Substitute the values of $a_{1}$ and $d$ into the formula. $a_{1} = 80$ $d = 1$ So, the expression for the nth term is: $a_{n} = 80 + (n-1)\times1$
Simplify nth term expression: Simplify the expression for the nth term. $\newline$ $a_n = 80 + n - 1$ $\newline$ $a_n = n + 79$

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