Find the Next Term 31 , 24 , 17

$31$ , $24$ , $17$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $- 7$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = - 7$

Step 2

This is the formula of an arithmetic sequence.

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

Step 3

Substitute in the values of $a_{1} = 31$ and $d = - 7$ .

$a_{n} = 31 - 7 (n - 1)$

Step 4

Simplify each term.

Apply the distributive property.

$a_{n} = 31 - 7 n - 7 \cdot - 1$

Multiply $- 7$ by $- 1$ .

$a_{n} = 31 - 7 n + 7$

Step 5

Add $31$ and $7$ .

$a_{n} = - 7 n + 38$

Step 6

Substitute in the value of $n$ to find the $n$ th term.

$a_{4} = - 7 \cdot 4 + 38$

Step 7

Multiply $- 7$ by $4$ .

$a_{4} = - 28 + 38$

Step 8

Add $- 28$ and $38$ .

$a_{4} = 10$

Find the Next Term 31 , 24 , 17

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