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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 $n = 1$ . $\newline$ $a_n = -5n - 4$ $\newline$ ___, _, _, _, ___

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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 = -5n - 4

\newline

_____, _____, _____, _____, _____

Find First Term: To find the first term in the sequence, substitute $n = 1$ into the formula $a_n = -5n - 4$ .
$a_1 = -5(1) - 4$
$a_1 = -5 - 4$
$a_1 = -9$
So, the first term of the sequence is $-9$ .
Find Second Term: To find the second term in the sequence, substitute $n = 2$ into the formula $a_n = -5n - 4$ . $\newline$ $a_2 = -5(2) - 4$ $\newline$ $a_2 = -10 - 4$ $\newline$ $a_2 = -14$ $\newline$ So, the second term of the sequence is $-14$ .
Find Third Term: To find the third term in the sequence, substitute $n = 3$ into the formula $a_n = -5n - 4$ . $\newline$ $a_3 = -5(3) - 4$ $\newline$ $a_3 = -15 - 4$ $\newline$ $a_3 = -19$ $\newline$ So, the third term of the sequence is $-19$ .
Find Fourth Term: To find the fourth term in the sequence, substitute $n = 4$ into the formula $a_n = -5n - 4$ . $a_4 = -5(4) - 4$ $a_4 = -20 - 4$ $a_4 = -24$ So, the fourth term of the sequence is $-24$ .
Find Fifth Term: To find the fifth term in the sequence, substitute $n = 5$ into the formula $a_n = -5n - 4$ . $a_5 = -5(5) - 4$ $a_5 = -25 - 4$ $a_5 = -29$ So, the fifth term of the sequence is $-29$ .

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