The sum of the first n terms in the infinite geometric sequence {1, 1/3, 1/9, 1/27, ...} is 121/81. Find n.

Edit: got it, it's 5 :D

AnonymousConfusedGuy
Jan 12, 2018

#1**+1 **

1*[1 - (1/3)^N] / [1 - 1/3] =121/81, solve for N

3/2 (1 - 3^(-N)) = 121/81

Multiply both sides by 2/3:

1 - 3^(-N) = 242/243

Subtract 1 from both sides:

-3^(-N) = -1/243

Multiply both sides by -1:

3^(-N) = 1/243

Take reciprocals of both sides:

3^N = 243

243 = 3^5:

3^N = 3^5

Equate exponents of 3 on both sides:

**N = 5**

Guest Jan 12, 2018

edited by
Guest
Jan 12, 2018