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Find the first five terms of the sequence defined below, where $n$ represents the position of a term in the sequence. Start with $n = 1$ . $\newline$ $a_n = 2n − 7$ $\newline$ ___, _, _, _, ___

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Evaluate explicit formulas for sequences

Full solution

Q. Find the first five terms of the sequence defined below, where

n

represents the position of a term in the sequence. Start with

n = 1

.

\newline

a_n = 2n − 7

\newline

_____, _____, _____, _____, _____

Find First Term: To find the first term of the sequence $a_1$ , substitute $n = 1$ into the formula $a_n = 2n − 7$ . $a_1 = 2(1) − 7$ $a_1 = 2 − 7$ $a_1 = -5$ So, the first term of the sequence is $-5$ .
Find Second Term: To find the second term of the sequence $a_2$ , substitute $n = 2$ into the formula $a_n = 2n − 7$ . $a_2 = 2(2) − 7$ $a_2 = 4 − 7$ $a_2 = -3$ So, the second term of the sequence is $-3$ .
Find Third Term: To find the third term of the sequence $a_3$ , substitute $n = 3$ into the formula $a_n = 2n − 7$ .
$a_3 = 2(3) − 7$
$a_3 = 6 − 7$
$a_3 = -1$
So, the third term of the sequence is $-1$ .
Find Fourth Term: To find the fourth term of the sequence $a_4$ , substitute $n = 4$ into the formula $a_n = 2n − 7$ . $a_4 = 2(4) − 7$ $a_4 = 8 − 7$ $a_4 = 1$ So, the fourth term of the sequence is $1$ .
Find Fifth Term: To find the fifth term of the sequence $a_5$ , substitute $n = 5$ into the formula $a_n = 2n − 7$ . $a_5 = 2(5) − 7$ $a_5 = 10 − 7$ $a_5 = 3$ So, the fifth term of the sequence is $3$ .

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