What is the 7th term of the geometric sequence where a1 = 1,024 and a4 = -16?

1 Answer
May 14, 2016

a_7 = 1024 (1/-4)^(6) = 1/4

Explanation:

Each term in a sequence - whether geometric or arithmetic can be given as a formula or as a value.
In a GP, a_n = ar^(n-1)

In this example, we have a_1 = -16 and a_4 = 1024, which can be written as ar^0 and ar^3

Let's divide them - formulae and values:

(ar^3)/(ar) = (-16)/(1024)

(cancelar^3)/(cancelar) = (-16)/1024 " " rArr r^3 = 1/(-64)

Finding the cube root gives r = 1/-4.

Now that we have a and r we can find the value of any term in the sequence.

a_7 = 1024 (1/-4)^(6) = 1/4