What is the 6th term of the geometric sequence where a1 = 625 and a3 = 25?

Question

anonymous · Answer

The formula to calculate a specific term in a geometric sequence is:

an = a1(r)^(n - 1)

But, you don't know what the ratio is. So solve for the ratio using the formula.

25 = 625(r)^(3 - 1)
25 = 625(r)^(2)
25 / 625 = (r)^2
0.04 = r^2
0.2 = r

So now you know what the ratio is, use the formula to find the 6th term of the series.

anonymous · Answer

0.0016?

anonymous · Answer

an = 625(0.2)^(6 - 1)
an = 625(0.2)^(5)
an = 625(0.00032)
an = 0.2

The 6th term in the series is 0.2.

anonymous · Answer

How did you get 0.0016? :)

anonymous · Answer

@TiffaniLynn13 Do you understand how I got 0.2? Or would you like me to explain further?