math
posted by mike .
if an is a geometric sequence where a1=4 and the sum of an=12. how would you find the common ratio of the sequence? please help

You must mean the infinite sum of ALL an, up to infinity. Partial sums cannot all be the same.
Let the common ratio be x.
4(1 + x + x^2 + ...) = 12
(1 + x + x^2 + ...) = 3
Now, recognize that the infinite series adds up to 1/(1x).
1/(1x) = 3
1/x = 1/3
x = 2/3
Respond to this Question
Similar Questions

maths
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 … 
Math
A sequence is formed by adding together the corresponding terms of a geometric sequence and and an arithmetic sequence.The common ratio of the geometric sequence is 2 and the common difference of the arithmetic sequence is 2.The first … 
Can someone help me?!
The 1st, 5th and 13th terms of an arithmetic sequence are the first three terms of a geometric sequence with a common ratio 2. If the 21st term of the arithmetic sequence is 72, calculate the sum of the first 10 terms of the geometric … 
Maths
Eric thinks of 2 sequences.One is geometric and the other arithmetic.Both sequences start with the number 3.The common ratio of the geometric sequence is the same as the common difference of the arithmetic sequence.If the 6th term … 
Maths
1..The first 2 terms of a geometric progression are the same as the first two terms of an arithmetic progression.The first term is 12 and is greater than the second term.The sum of the first 3 terms od the arithmetic progression is … 
geometric sequence
The sum of the 2nd and 5th terms of a geometric sequence is 3.5. The sum of the 3rd and 6th is 7. Determine the ratio r of the sequence and the first term a. 
Math
1. Find the sum of the first five terms of the sequence 2/3, 2, 6, 18, ..... My answer is 242. Am I right? 
MATH
A new sequence is formed by adding together the corresponding terms of a geometric sequence and an arithmetric sequence. the geometric sequence has a common ratio of 3 and the arthmetric sequence has a common difference of 2. The … 
math
The 1st,5th,13th term of an arithmetic sequence are the first 3 terms of geometric sequence with a common ratio of 2. If the 21st term of the arithmetic sequence is 72, calculate the sum of the first 10 terms of the geometric sequence. 
precalculus urgent
Please help me here as well to clarify more my understanding. Let a1, a2, a3, . . . be a geometric sequence with initial term a and common ratio r. Show that a1^2, a2^2, a3^2, . . . is also a geometric sequence by finding its common …