Question 1165566
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(C)  Your part (C) is NOT complete.  <U>See how it SHOULD be done.</U>


     First term is 25 and third term is 900.


     It means that  {{{a[3]}}} = {{{a[1]*r^2}}},  where "r" is the common ratio.


     Substitute here {{{a[3]}}} = 900;  {{{a[1]}}} = 25.  You will get


         900 = {{{25*r^2}}}  ---->  {{{r^2}}} = {{{900/25}}} = 36  ---->  r = {{{sqrt(36)}}} = +/- 6.


     It means that r may have TWO values, 6 and -6.


     These two values of "r" create TWO DIFFERENT geometric sequences.
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The same is with part (E).


<pre>
(E)  Your part (E) is NOT complete.  <U>See how it SHOULD be done.</U>


     First term is -5 and fifth term is -6480.


     It means that  {{{a[5]}}} = {{{a[1]*r^4}}},  where "r" is the common ratio.


     Substitute here {{{a[3]}}} = -6480;  {{{a[1]}}} = -5.  You will get


         -6480 = {{{(-5)*r^4}}}  ---->  {{{r^4}}} = {{{(-6480)/(-5)}}} = 1296  ---->  r = {{{root(4,1296)}}} = +/- 6.


     It means that r may have TWO values, 6 and -6.   (if we restrict ourselves by real numbers). 


     These two values of "r" create TWO DIFFERENT geometric sequences.
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You may often meet such problems and such questions.


Their destination is to check if you are able to analyze the problems accurately.


So be aware about it.