Find the # of terms in a GS (geometric sequence)?

Question

Que: Find the # of terms in a GS (geometric sequence)

2, 10, 50,... 1250

So, the formula that should be used is: u1 x r^n-1 ???

(the one in the U is sub!!)

U1 x r^n-1

= 2 x 5^n-1

= ???

How to find the N?

Many thanks!!!

Answer 1

If n is the number of terms:

1250 = 2 * 5^(n - 1)

625 = 5^(n - 1)

You can solve that by inspection, as successive powers of 5 are:

5, 25, 125, 625.

n - 1 = 4

n = 5.

If it weren't so simple, you would take logs:

log(625) = (n - 1)log(5)

n - 1 = log(625) / log(5)

n = 1 + log(625) / log(5)

= 5.