Question

The geometric sequence that tells the perimeter of each stage in the building of Koch's snowflake has a first term of 3 and a ratio of 4/3.

At the 18th stage in the construction of this snowflake, the length of each tiny side would be about the size of an atom! Using the explicit formula for the nth term of a geometric sequence, what is the length of the perimeter a18 to the nearest whole number?

A. 399
B. 299
C. 200
D. 133
E. 99

Answer 1

an = a1 * r^(n-1)
n = term to find = 18
a1 = first term = 3
r = common ratio = 4/3
now we sub

a18 = 3 * 4/3^(18 - 1)
a18 = 3 * 4/3^17
a18 = 3 * 133
a18 = 399