Question

Find the 6th term of a geometric sequence t3 = 444 and t7 = 7104.

Answer 1

If we divide the 7th term by the third it gives us r^4   (  common ratio to power 4).

r^4 = 7104/444 =   16

so r =  4th root of 16  = 2

So 6th term will be the 7th term / 2 = 7104 / 2 =  3552

Answer 2

Given the value of t3 and t7, and t7 = t3 * r^4, where r represents the geometric quotient. 

So 7104 = 444 * r^4 -> solve for r, you will get r = 2 or -2

So, for r = 2, t6 = t7 / r = 7104 / 2 = 3552

For r = -2, t6 = -3552