SOLUTION: The sum of the first and 4th term of a G.P is -1575 while the sum of the 3rd and 6th term is -25200. Find the first term, common ratio, and the sum of the 4th to 20th term inclusiv

Question 1169187: The sum of the first and 4th term of a G.P is -1575 while the sum of the 3rd and 6th term is -25200. Find the first term, common ratio, and the sum of the 4th to 20th term inclusive.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

a, ar, ar^2, ar^3, ar^4, ar^5, ar^6, ...

The sum of the 1st and 4th terms is -1575

The sum of the 3rd and 6th terms is -25200

Factor out the common term a^2 in the second equation.

The common ratio r is either 4 or -4.

Suppose r=4. Then the sum of the 1st and 4th terms is

That gives a non-integer value for the first term a.

So let's try r=-4.

The first term is a=25; the common ratio is a=-4.

The first few terms are

25, -100, 400, -1600, 6400, -25600, ....

To find the sum of the 4th through 20th terms, find the sum of the first 20 terms and subtract the sum of the first 3 terms.

The 20th term of the sequence is , which is about -6.87x10^12, so you will need a calculator that can handle large numbers if you need to get an exact answer. An excel spreadsheet is one option that will work nicely.

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