what is the 8th term of 15,18,108/5

Answer 1

This is a sequence with a common multiplier, I think it is called the common ratio.

Take 2nd term and divide it by the 1st term and you will get r, the common ratio.

18/15 = 6/5

Now check. 1st term * 6/5 = 15 * 6/5 = 18 (2nd term)

2nd term * 6/5 = 18 * 6/5 = 108/5 (3rd term)

3rd term * 6/5 = (108/5)(6/5) = 648/25 (4th term)

4th term * 6/5 = (648/5)(6/5) = 3888/125 (5th term)

5th term * 6/5 = (3888/125)(6/5) = 23,328/625 (6th term)

6th term * 6/5 = (23,328/625)(6/5) = 139,968/3125 (7th term)

7th term * 6/5 = (139,968/3125)(6/5) = 839,808/15,625 (8th term)

So the answer is 839,808/15,625

And we can check by using the formula for geometric sequences/series:

a_n = a₁ r^(n-1)

Here n=8 (because we want the 8th term)

a₁ = 15 (the first term)

r = 6/5 (as we calculated above)

n-1 = 7

Putting all this into the formula, we get that

a₈ = (15)(6/5)⁷ = (15)(279,936/78,125) = 839,808/15,625 (same answer as doing it "by hand")