Question 1202480
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The sum of a geometric sequence 2 - 6 + 18 - 54 + ... - tn is - 29524. 
Find the number of terms.
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<pre>
This geometric progression has the first term a= 2 and the common ratio -3.


Use the general formula for the sum of the first n terms

    {{{S[n]}}} = {{{a*((r^n-1)/(r-1))}}}.


It gives

    -29524 = {{{2*(((-3)^n-1)/((-3)-1))}}}.


Simplify and find n

    {{{((-29524)*(-4))/2}}} = {{{(-3)^n-1}}}

    59048 = {{{(-3)^n-1}}}

    59048 + 1 = {{{(-3)^n}}}

    59049 = {{{(-3)^n}}}

    {{{(-3)^10}}} = {{{(-3)^n}}}


It implies  n= 10.


<U>ANSWER</U>.  The number of terms is 10.
</pre>

Solved.