Identify the Progression -7.4 , -21.2 , -35 , -48.8 , -62.6

$- 7.4$ , $- 21.2$ , $- 35$ , $- 48.8$ , $- 62.6$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $- 13.8$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = - 13.8$

Step 2

This is the formula of an arithmetic sequence.

$a_{n} = a_{1} + d (n - 1)$

Step 3

Substitute in the values of $a_{1} = - 7.4$ and $d = - 13.8$ .

$a_{n} = - 7.4 - 13.8 (n - 1)$

Step 4

Simplify each term.

Apply the distributive property.

$a_{n} = - 7.4 - 13.8 n - 13.8 \cdot - 1$

Multiply $- 13.8$ by $- 1$ .

$a_{n} = - 7.4 - 13.8 n + 13.8$

Step 5

Add $- 7.4$ and $13.8$ .

$a_{n} = - 13.8 n + 6.4$

Identify the Progression -7.4 , -21.2 , -35 , -48.8 , -62.6

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