Find the geometric sum: 12 + 36 + 108 + ... + 78,732. 39,360 118,092 1,062,876 354,288

This is a geometric sequence with an initial term of 12 and a common ratio of 3.

The rule for a geometric sequence is:

a (n) = ar^ (n-1) we are told that the last term is 78732 so we can find the number of terms in the sequence ...

78732=12 (3) ^ (n-1) divide both sides by 12

6561=3^ (n-1) take the natural log of both sides

ln6561 = (n-1) ln3 divide both sides by ln3

ln6561/ln3=n-1 add 1 to both sides

ln6561/ln3 + 1=n

9=n so there are 9 terms in the sequence.

The sum of any geometric sequence is:

s (n) = a (1-r^n) / (1-r), in this case a=12, r=3, and n=9 so

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

s (9) = 12 (1-19683) / (-2)

s (9) = - 6 (-19682)

s (9) = 118092