Question 1137520

 Given the sequence: {{{2}}}, {{{6}}}, {{{18}}}, {{{54}}}, …. 

a. What is the common ratio? 

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


b. What is the recursive formula? 

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

{{{a[1]=2}}}, {{{r=3}}}

{{{a[n]=2*3^(n-1)}}} for {{{n}}}={{{1}}},{{{2}}},{{{3}}},....


check the formula:

{{{a[1]=2*3^(1-1)=2*3^0=2*1=2}}}

{{{a[2]=2*3^(2-1)=2*3^1=2*3=6}}}

{{{a[3]=2*3^(3-1)=2*3^2=2*9=18}}}

{{{a[4]=2*3^(4-1)=2*3^3=2*27=54}}}