Posted by **jen** on Friday, October 19, 2007 at 10:39pm.

The common ratio r of a geometric sequence satisfies the quadratic equation 2r squared - 3r -2 = 0. If the sum to infinity of the same sequence is 6, explain why, in this case, r can only take on one value, and hence state the common ratio, r. Also, show that the first term 'a' of this sequence is 9.

Thanks so much xx

- maths -
**drwls**, Saturday, October 20, 2007 at 2:24am
The only solutions to 2r^2 - 3r -2 = 0 are

r = 2 and r = -1/2. You can prove that by factoring the equation.

The sequence a + ra + r^2 a + ...will not converge if r = 2. Therefore r must be -1/2.

Use the fact that the sum is 6 to figure out the first term, a

6 = a (1 -1/2 + 1/4 -1/8 + ...)

= a [1/(1 + (1/2))] = a*(2/3)

a = 9

## Answer This Question

## Related Questions

- Maths - 1..The first 2 terms of a geometric progression are the same as the ...
- Maths - Eric thinks of 2 sequences.One is geometric and the other arithmetic....
- pre-calculus urgent - Please help me here as well to clarify more my ...
- MATH - A new sequence is formed by adding together the corresponding terms of a ...
- Math - A sequence is formed by adding together the corresponding terms of a ...
- Math - first three terms of a geometric sequence are the same as the 1st, 9th ...
- geometric sequence - The sum of the 2nd and 5th terms of a geometric sequence is...
- Can someone help me?! - The 1st, 5th and 13th terms of an arithmetic sequence ...
- math - The 1st,5th,13th term of an arithmetic sequence are the first 3 terms of ...
- math - if an is a geometric sequence where a1=4 and the sum of an=12. how would ...

More Related Questions