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

2 Answers
Nov 16, 2016

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!

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*(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.