Question

Identify the 8th term of the geometric sequence -2, -12, -72

Answer 1

The Nth term in any geometric sequence is \[ar ^{n-1}\]
where a= the first number of the sequence and r = the difference between each sequence of the term.

In this geometric sequence, we see that a= -2.
To find the difference between each sequence, we divide any two consecutive terms (not it must always be the number later in the sequence/the number earlier, meaning for example, divide the 3rd term over the 2nd term instead of the 2nd term of the 3rd term)
So r = -12/-2 = 6

Therefore the 8th term = \[-2 \times 6^{8-1} =-559872\]