# How do you complete the statement for the arithmetic sequence: 170 is the __ term of -4, 2, 8, ...?

Nov 16, 2016

30th.

#### Explanation:

This is an arithmetic sequence with first term $- 4$, common difference $6$ and nth term $170$.

${t}_{n} = a + \left(n - 1\right) d$

$170 = - 4 + \left(n - 1\right) 6$

$170 = - 4 + 6 n - 6$

$170 + 10 = 6 n$

$180 = 6 n$

$n = 30$

Hopefully this helps!

Nov 16, 2016

170 is the 30th term of the sequence -4, 2, 8, ...

#### Explanation:

First, you need to determine what the likely sequence is. With only the three given numbers, it looks like each one is the previous one plus 6. Algebraically, the sequence is x_n = (x_(n+1)*6, with an ‘offset’ to start it at -4:

${x}_{n} = - 4 + 6 \cdot \left(n - 1\right)$

Now we can put in the value of 170 and solve for the placement in the sequence.

$170 = - 4 + 6 \cdot \left(n - 1\right)$
$174 = 6 \cdot \left(n - 1\right)$

n-1 = $\frac{174}{6}$ = 29
Because ‘29’ is the (n-1)th term in the series, the value of 170 is the 30th term in the series.