# SOLUTION: 2) Use the geometric sequence of numbers 1, 3, 9, 27, … to find the following: a) What is r, the ratio between 2 consecutive terms? Answer: Show work in this space

Algebra ->  Algebra  -> Sequences-and-series -> SOLUTION: 2) Use the geometric sequence of numbers 1, 3, 9, 27, … to find the following: a) What is r, the ratio between 2 consecutive terms? Answer: Show work in this space      Log On

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 Algebra: Sequences of numbers, series and how to sum them Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Sequences-and-series Question 78546: 2) Use the geometric sequence of numbers 1, 3, 9, 27, … to find the following: a) What is r, the ratio between 2 consecutive terms? Answer: Show work in this space. b) Using the formula for the nth term of a geometric sequence, what is the 10th term? Answer: Show work in this space. c) Using the formula for the sum of a geometric sequence, what is the sum of the first 10 terms? Answer: Show work in this space. Answer by jim_thompson5910(28598)   (Show Source): You can put this solution on YOUR website!a) The ratio r is the factor needed to go from term to term. To find the factor, divide any term by its previous term. So I chose 3 as the first term to be divided by 1 Ratio r: pick any nth term and any previous term, such as the 2nd and 1st term. I can also do it with 27 and 9 and it will still give me the same value So r=3 b) Since we are multiplying by r each term, our sequence is simply So to find the nth term (), we simply multiply the previous term () by r. So if we start at 1, to get to 3 we multiply 1 by r=3 Now to go from 3 to 9 we multiply by r again Now to go from 9 to 27 we multiply by r again Notice that for the 1st term 3 we have only 1 r, 2nd term we have 2 r's, etc. So the term we have determines the number of r's. In other words, the nth term is So our sequence is Now let n=9 to find the 10th term (we started at n=0) So the 10th term is 19,683 c) The sum of the first ten terms can be found by using So let r=3 So the sum of the first ten terms are 29,524