Find the sum of the geometric sum: 12 36 108 ... 78,732

Ok, geometric

seems to be multiply by 3 each time

hmm, so

the sum of a geometric sequence where a1 is the first term, n is which term and r=common ratio

Sn=a1 (1-r^n) / (1-r)

so

we need to find which term

so

an=a1 (r) ^ (n-1)

a1=first term=12

and common ratio is 3=r

and the nth term is 78732

78732=12 (3) ^ (n-1)

78732=12 (1/3) (3^n)

78732=4 (3^n)

divide both sides by 4

19683=3^n

use math to solve and get

9=n

so that was the 9th term

a1=12

r=3

n=9

S9=12 (1-3^9) / (1-3)

S9=12 (1-19683) / (-2)

S9=-6 (-19682)

S9=118092

the sum is 118092