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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. $\newline$ $74, 75, 76, 77, \ldots$ $\newline$ $a_n =$ _____

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Write variable expressions for arithmetic sequences

Full solution

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

74, 75, 76, 77, \ldots

\newline

a_n =

_____

Identify Sequence Type: We have the sequence: $74, 75, 76, 77, \ldots$ $\newline$ First, we need to determine if the sequence is arithmetic or geometric. $\newline$ By observing the sequence, we can see that there is a constant difference between consecutive terms, which means the sequence is arithmetic.
Find First Term and Difference: Next, we need to identify the first term of the sequence, which is $a_1$ , and the common difference, $d$ . The first term, $a_1$ , is $74$ . To find the common difference, $d$ , we subtract the first term from the second term: $d = 75 - 74 = 1$ .
Write General Formula: Now, we can write the general formula for the $n$ th term of an arithmetic sequence, which is: $\newline$ $a_n = a_1 + (n-1)d$ $\newline$ We already know that $a_1 = 74$ and $d = 1$ .
Substitute Values and Simplify: Substitute the values of $a_{1}$ and $d$ into the formula to get the expression for the nth term: $\newline$ $a_{n} = 74 + (n-1)\times1$ $\newline$ Simplify the expression: $\newline$ $a_{n} = 74 + n - 1$ $\newline$ $a_{n} = n + 73$

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