Question 937701


If the sequence is geometric, then there is a common ratio, we must think in terms of multiplication previous term by common ratio {{{r}}} to get next term in sequence.

The r-value can be calculated by dividing {{{any}}}{{{ two}}}{{{ consecutive}}} terms in a geometric sequence. 

The formula for calculating  the Common Ratio {{{r}}} is:


{{{r = (nth_ term)/((n-1)th _term)}}}



1.  
{{{2}}}, {{{4}}}, {{{7}}}, {{{11}}}, {{{16}}}, {{{22}}}, {{{29}}}, {{{37}}}, … 



{{{r = 4/2=2}}}

{{{r = 7/4=1.75}}}

{{{r = 11/7=1.571428571428571}}}

 there is no common ratio {{{r}}}, {{{not}}} a geometric sequence



2.
{{{4}}}, {{{8}}}, {{{14}}}, {{{22}}}, {{{38}}}, … 



{{{r = 8/4=2}}}

{{{r = 14/8=1.75}}}

{{{r = 22/14=1.571428571428571}}}

there is no common ratio {{{r}}}, {{{not}}} a geometric sequence


3.
{{{6}}}, {{{9}}}, {{{12}}}, {{{15}}}, {{{18}}}, {{{21}}}, … 


{{{r = 9/6=3/2}}}

{{{r = 12/9=4/3}}}

{{{r = 15/12=5/4}}}

there is no common ratio {{{r}}}, {{{not}}} a geometric sequence


4.

9, 27, 81, 343, 729, …

{{{r = 27/9=3}}}

{{{r = 81/27=3}}}

{{{r = 343/81=4.24}}}  

{{{r = 729/343=2.12536443148688}}} there is no common ratio {{{r}}}, {{{not}}} a geometric sequence


since you have to have one solution, I think the  term {{{ 343}}} is wrong because first three terms have common ratio {{{3}}},if we multiply {{{81*3}}} we got {{{243}}} and {{{r =243/81=3}}}  

and next one will be {{{r = 729/243=3}}}

there is common ratio {{{r=3}}}, means the sequence {{{9}}}, {{{27}}}, {{{81}}}, {{{243}}}, {{{729}}}, … {{{IS}}} a geometric sequence