# How to find the common ratio of geometric sequence when the sum of 5th term to 8th term is twice the first four terms?

The common ratio is

The sequence of geometric shapes is

Consequently,

So,

By signing up, you agree to our Terms of Service and Privacy Policy

We have,

Given the information, we discover

By signing up, you agree to our Terms of Service and Privacy Policy

To find the common ratio of a geometric sequence when the sum of the 5th term to the 8th term is twice the sum of the first four terms:

- Let the first term of the geometric sequence be ( a ) and the common ratio be ( r ).
- Write out the expressions for the terms of the sequence: ( a, ar, ar^2, ar^3, ar^4, ar^5, ar^6, ar^7 ).
- The sum of the first four terms is ( S_4 = a + ar + ar^2 + ar^3 ).
- The sum of the 5th term to the 8th term is ( S_{5-8} = ar^4 + ar^5 + ar^6 + ar^7 ).
- Given that ( S_{5-8} = 2S_4 ), set up the equation: ( ar^4 + ar^5 + ar^6 + ar^7 = 2(a + ar + ar^2 + ar^3) ).
- Simplify the equation and solve for ( r ).
- Once you have found the value of ( r ), you can use it to find any other term of the sequence if needed.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- What is the 28th term of the sequence -6.4, -3.8, -1.2, 1.4?
- ?How do you find the sum of the infinite geometric series 0.03, 0.03, 0.003?
- How do you write the first five terms of the sequence #3n^2+4# using the nth term rule?
- What is the sum of the geometric series #Sigma 6(2)^n# from n=1 to 10?
- What is the sum of a 7–term geometric series if the first term is –11, the last term is –171,875, and the common ratio is –5?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7