Find the 6th Term 17 , 8 , -1 , -10

$17$ , $8$ , $- 1$ , $- 10$

Step 1

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $- 9$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = - 9$

Step 2

This is the formula of an arithmetic sequence.

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

Step 3

Substitute in the values of $a_{1} = 17$ and $d = - 9$ .

$a_{n} = 17 - 9 (n - 1)$

Step 4

Simplify each term.

Apply the distributive property.

$a_{n} = 17 - 9 n - 9 \cdot - 1$

Multiply $- 9$ by $- 1$ .

$a_{n} = 17 - 9 n + 9$

Step 5

Add $17$ and $9$ .

$a_{n} = - 9 n + 26$

Step 6

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

$a_{6} = - 9 \cdot 6 + 26$

Step 7

Multiply $- 9$ by $6$ .

$a_{6} = - 54 + 26$

Step 8

Add $- 54$ and $26$ .

$a_{6} = - 28$

Find the 6th Term 17 , 8 , -1 , -10

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