SOLUTION: a geometric sequence has a sixth term of 24 and a common ratio of 2/3. find the first three terms

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Question 825215: a geometric sequence has a sixth term of 24 and a common ratio of 2/3. find the first three terms
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = the first term.
Term definition is the term number n is a%282%2F3%29%5E%28n-1%29;

Given term at n=6 is 24, means a%282%2F3%29%5E%286-1%29=24;
a%282%2F3%29%5E5=24

24=12*2=2*2*3*2=2*2*2*3=2%5E3%2A3

You could start with 24, multiply it by 3%2F2 until you do it six times, and that should be your "a", first term.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
a geometric sequence has a sixth term of 24 and a common ratio of 2/3. find the first three terms 


GP formula: a%5Bn%5D+=+a%5B1%5Dr%5E%28n+-+1%29

a%5B6%5D+=+a%5B1%5D%282%2F3%29%5E%286+-+1%29___Substituting 6 for n, and 2%2F3 for r

24+=+a%5B1%5D%282%2F3%29%5E5_____Substituting 24 for a%5Bn%5D

24+=+a%5B1%5D%2832%2F243%29

a%5B1%5D+=+24÷32%2F243

a%5B1%5D+=+24%28243%2F32%29

a%5B1%5D+=+3cross%2824%29%28243%2F4cross%2832%29%29

a%5B1%5D+=+729%2F4%29, or highlight_green%28a%5B1%5D+=+182.25%29



The first term, or a%5B1%5D(182.25), and the common ratio, or r (2%2F3), should be substituted into the GP formula,

a%5Bn%5D+=+a%5B1%5Dr%5E%28n+-+1%29 to determine the 2nd term (a%5B2%5D), and 3rd term (a%5B3%5D).



You'll then have all 3 terms.



You can do the check!! 



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