Find the first 4 terms of the infinite geometric series if S = 33/4 and r = 1/3

Answer 1

The formula for the sum of an infinite geometric sequence is S = a1/(1-r), where a1 is the first term and r is the common ratio.

Since we are given S and r, we can use algebra to solve for a1 as follows:

S = a1/(1-r)
33/4 = a1/(1-1/3)
33/4 = a1/(2/3)
a1 = (33/4) * (2/3)
a1 = 22/4
a1 = 11/2

Therefore, the first term is 11/2 and the common ratio is 1/3. To find the first 4 terms, we can use the formula for the nth term of a geometric sequence:

an = a1 * r^(n-1)

So:

a2 = 11/2 * (1/3)^1 = 11/6
a3 = 11/2 * (1/3)^2 = 11/18
a4 = 11/2 * (1/3)^3 = 11/54

Therefore, the first 4 terms are:

11/2, 11/6, 11/18, 11/54.