What are the first 3 terms of the series if the first term is 3? VERY HARD

Question

For the Geometic Series, S4/S8 = 1/17

What are the first three terms of the series if the first term is 3??

Answer 1

Step 1:

Sum of the n terms of the geometric series where

Here, is the first term and r is the common ratio.

Find the sum of 4 terms:

Find the sum of 8 terms:

Solve this equation.

Step 2:

Find the first term by using the nth term of the geometric series:

Substitute , , and .

Find the second term by using the nth term of the geometric series:

Substitute , , and .

Find the third term by using the nth term of the geometric series:

Substitute , , and .

Solution:

First three terms are 3, 6, and 12.