Identify the Sequence 26 , 10 , -6 , -22

$26$ , $10$ , $- 6$ , $- 22$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $- 16$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = - 16$

Step 2

This is the formula of an arithmetic sequence.

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

Step 3

Substitute in the values of $a_{1} = 26$ and $d = - 16$ .

$a_{n} = 26 - 16 (n - 1)$

Step 4

Simplify each term.

Apply the distributive property.

$a_{n} = 26 - 16 n - 16 \cdot - 1$

Multiply $- 16$ by $- 1$ .

$a_{n} = 26 - 16 n + 16$

Step 5

Add $26$ and $16$ .

$a_{n} = - 16 n + 42$

Identify the Sequence 26 , 10 , -6 , -22

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