Find the 6th Term -62 , -47 , -32 , -17 , -2

$- 62$ , $- 47$ , $- 32$ , $- 17$ , $- 2$

This is an arithmetic sequence since there is a common difference between each term. In this case, adding $15$ to the previous term in the sequence gives the next term. In other words, $a_{n} = a_{1} + d (n - 1)$ .

Arithmetic Sequence: $d = 15$

This is the formula of an arithmetic sequence.

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

Substitute in the values of $a_{1} = - 62$ and $d = 15$ .

$a_{n} = - 62 + 15 (n - 1)$

Simplify each term.

Apply the distributive property.

$a_{n} = - 62 + 15 n + 15 \cdot - 1$

Multiply $15$ by $- 1$ .

$a_{n} = - 62 + 15 n - 15$

Subtract $15$ from $- 62$ .

$a_{n} = 15 n - 77$

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

$a_{6} = 15 (6) - 77$

Multiply $15$ by $6$ .

$a_{6} = 90 - 77$

Subtract $77$ from $90$ .

$a_{6} = 13$

Find the 6th Term -62 , -47 , -32 , -17 , -2

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