SOLUTION: In a geometric series, the sum of the first three terms is 304, and the sum of the first six terms is 1330. Find the sum of the first seven terms.

Question 898542: In a geometric series, the sum of the first three terms is 304, and the sum of the first six terms is 1330. Find the sum of the first seven terms.
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!
In a geometric series, the sum of the first three terms is 304,

(1)

and the sum of the first six terms is 1330.

So the sum of the 3rd, 4th and 5th terms only is 1330-304 = 1026



(2)   

Dividing equals by equals, equation (2) by equation (1)

    

    

    

Taking cube roots of both sides

    

Substitute in equation (1)

(1)   

      

      

Multiply the terms in the parentheses and the right side by 4
to clear of fractions:

      

      

Divide both sides by 19

Find the sum of the first seven terms.







Multiply the top out, the 16 goes into the 128 2 times,
and write the 1 on the bottom as 





Multiply top and bottom by 2


 




Edwin

RELATED QUESTIONS
The sum of the first three terms of a geometric sequence is 8 and the sum of the first... (answered by mananth,ikleyn,Edwin McCravy,greenestamps)

A geometric series has 8 terms whose sum of the first three terms is 13/9 and the sum of... (answered by KMST)

In a geometric series, the 9th term is equal to 8 times the 6th term, while the sum of... (answered by robertb)

In a geometric sequence of real numbers, the sum of the first two terms is 11 and the sum (answered by ikleyn)

In a geometric sequence of real numbers, the sum of the first two terms is 7 and the... (answered by ikleyn)

the sum of the first two terms of a geometric series is 1 and the sum of its first four... (answered by josgarithmetic)

In a geometric series with first term, a and common ratio, r (where r is real and... (answered by greenestamps)

The sum of the first 4 terms of a geometric series is 15 and the sum of the next 4 terms... (answered by ikleyn)

Find the sum of the first 8 terms in the geometric series 1-4+16-64+... (answered by richwmiller)