SOLUTION: sum of a geometric series is 46.5. The first term of the series is 24​, and its common ratio is 0.5. How many terms are there in the​ series?

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Question 1156304: sum of a geometric series is 46.5. The first term of the series is 24​, and its common ratio is 0.5. How many terms are there in the​ series?
Found 2 solutions by jim_thompson5910, MathTherapy:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!

n = number of terms = unknown
S = 46.5 = sum of the first n terms
a = 24 = first term
r = 0.5 = common ratio

Formula used to add the first n terms of a geometric sequence

Substitution



Multiply both sides by 0.5





Divide both sides by 24



Isolate the term 0.5^n



Apply logs to both sides

We do so to be able to pull the exponent n down.

Divide both sides by log(0.5)

Use a calculator

Answer: 5 terms

The first five terms are: {24, 12, 6, 3, 1.5}
Each new term is found by multiplying the previous term by the common ratio 0.5

Those five terms add to
24 + 12 + 6 + 3 + 1.5 = 46.5
which confirms our answer.

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

sum of a geometric series is 46.5. The first term of the series is 24​, and its common ratio is 0.5. How many terms are there in the​ series?
Formula for sum of a G.P.: 

                           

                           

                           

                           Number of terms, or  

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