Question 1193516
.
Find the number of terms in this geometric series
-4 + 16 - 64 + 256..., where Sn=52428
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<pre>
Use the formula for the sum of a geometric progression

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


where "a" is the first term and "r" is the common ratio.


In your case a= -4, r= -4, so the formula is

    52428 = {{{(-4)*(((-4)^n-1)/(-4-1))}}},

or

    52428 = {{{(-4)*(((-4)^n-1)/(-5))}}}.


From this formula,

    {{{(-4)^n - 1}}} = {{{52428*((-5)/(-4))}}} = 65535

    {{{(-4)^n}}} = 65535 + 1 = 65536 = {{{4^8}}},

so

    n = 8.


<U>ANSWER</U>.  n = 8.
</pre>

Solved.


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On geometric progressions, &nbsp;see introductory lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Geometric-progressions.lesson>Geometric progressions</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/The-proofs-of-the-formulas-for-geometric-progressions.lesson>The proofs of the formulas for geometric progressions</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Problems-on-geometric-progressions.lesson>Problems on geometric progressions</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Word-problems-on-geometric-progressions.lesson>Word problems on geometric progressions</A>

in this site.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic 
<U>"Geometric progressions"</U>.


Save the link to this textbook together with its description


Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson


into your archive and use when it is needed.