Question 939169


first find differences between each two given terms and go until you get all differences equal

{{{8}}}-----{{{43}}}-----{{{138}}}-------{{{323}}}-----{{{628}}}-----{{{1083}}}-----{{{1718}}}....

---{{{35}}}-----{{{95}}}------{{{185}}}------{{{305}}}-----{{{455}}}-----{{{635}}}------

-------{{{60}}}-----{{{90}}}------{{{120}}}-----{{{150}}}-----{{{180}}}------

-----------{{{30}}}-----{{{30}}}------{{{30}}}-------{{{30}}}------=> third differences same, means we have {{{third}}} degree function

first term is {{{8}}} and it can be written as {{{5+3}}}

if we have  third degree function {{{n^3}}} to get first term if {{{n}}} starts with {{{1}}} we can write it as  {{{5n^3+3}}}

so, general equation for nth term is:


{{{a[n] = 5n^3+3 }}} where {{{n}}}={{{1}}},{{{2}}},{{{3}}},........


check: 

{{{a[n] = 5n^3+3 }}} if {{{n=1}}}

{{{a[1] = 5(1)^3+3 }}}
{{{a[1] = 5(1)+3 }}}
{{{a[1] = 5+3 }}}
{{{a[1] = 8 }}}


{{{a[n] = 5n^3+3 }}} if {{{n=2}}}

{{{a[2] = 5(2)^3+3 }}}
{{{a[2] = 5(8)+3 }}}
{{{a[2] = 40+3 }}}
{{{a[2] = 43 }}}


{{{a[n] = 5n^3+3 }}} if {{{n=3}}}

{{{a[3] = 5(3)^3+3 }}}
{{{a[3] = 5(27)+3 }}}
{{{a[3] = 135+3 }}}
{{{a[3] = 138 }}}