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 -44, common difference 66 and nth term 170170.

t_n = a+ (n - 1)dtn=a+(n1)d

170 = -4 + (n - 1)6170=4+(n1)6

170 = -4 + 6n - 6170=4+6n6

170 + 10 = 6n170+10=6n

180 = 6n180=6n

n = 30n=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)*6xn=(xn+16, with an ‘offset’ to start it at -4:

x_n = -4 + 6*(n-1) xn=4+6(n1)

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

170 = -4 + 6*(n-1)170=4+6(n1)
174 = 6*(n-1)174=6(n1)

n-1 = 174/61746 = 29
Because ‘29’ is the (n-1)th term in the series, the value of 170 is the 30th term in the series.