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

2 Answers
Nov 16, 2016

Answer:

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

Answer:

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.