Math question 3 c?

using the formula for the sum of the first n terms, of a goemetric sequence, [a (r^n)] / [r-1] what is the sum of the first 12 terms?





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Math question 3 c?
Let S = a + ar + ar^2 + ar^3 + ... + ar^n, where a is the first term and r is the common ratio. Note that ar^n is the n+1st term of this sum. Multiply S by r obtaining


rS = ar + ar^2 +ar^3 +... + ar^n + ar^(n+1). Then subtract, yeilding S - rS = a - a^r(n+1). or


S(1-r) = a(1-r^(n+1)).


Dividing, S = a(1-r^(n+1))/(1-r) as the sum of the first n+1 terms.


So, the sum of the first m terms is


S = a(1-r^m)/(1-r).


If m = 12, this becomes


S = a(1-r^12)/(1-r).
Reply:replace n with 12