Question 1156304
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n = number of terms = unknown
S = 46.5 = sum of the first n terms
a = 24 = first term
r = 0.5 = common ratio


{{{S = (a(1-r^n))/(1-r)}}} Formula used to add the first n terms of a geometric sequence


{{{46.5 = (24(1-0.5^n))/(1-0.5)}}} Substitution


{{{46.5 = (24(1-0.5^n))/0.5}}}


{{{46.5*0.5 = 24(1-0.5^n)}}} Multiply both sides by 0.5


{{{23.25 = 24(1-0.5^n)}}}


{{{24(1-0.5^n) = 23.25}}}


{{{1-0.5^n = 23.25/24}}} Divide both sides by 24


{{{1-0.5^n = 0.96875}}}


{{{0.5^n = 1-0.96875}}} Isolate the term 0.5^n


{{{0.5^n = 0.03125}}}


{{{log((0.5^n)) = log((0.03125))}}} Apply logs to both sides


{{{n*log((0.5)) = log((0.03125))}}} We do so to be able to pull the exponent n down. 


{{{n = log((0.03125))/log((0.5))}}} Divide both sides by log(0.5)


{{{n = 5}}} Use a calculator


Answer: <font color=red>5 terms</font>


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. 
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