Question 933534
{{{a[2]-a[1]=3}}}, {{{a[3]-a[2]=9}}}, {{{a[4]-a[3]=15}}}, {{{a[5]-a[4]=21}}},

3, 9, 15, 21

Since we are given that 

{{{a[2]+a[1]=21}}}, we have the system

{{{system(a[2]-a[1]=3,a[2]+a[1]=21)}}}

Solve that system and get {{{a[2]=12}}} and {{{a[1]=9}}}, so

{{{a[3]-a[2]=9}}}
{{{a[3]-12=9}}}
{{{a[3]=21}}}

{{{a[4]-a[3]=15}}}, 
{{{a[4]-a[3]=15}}}
{{{a[4]-21=15}}}
{{{a[4]=36}}}

{{{a[5]-a[4]=21}}},
{{{a[5]-36=21}}}
{{{a[5]=57}}}

The general term, BTW, is {{{3(n^2-2n+4)}}}

Edwin