Question

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

Answer 1

30th.

Explanation:

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

`t_n = a+ (n - 1)d`

`170 = -4 + (n - 1)6`

`170 = -4 + 6n - 6`

`170 + 10 = 6n`

`180 = 6n`

`n = 30`

Hopefully this helps!

Answer 2

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*(n-1)`

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

`170 = -4 + 6*(n-1)`
`174 = 6*(n-1)`

n-1 = `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.