Question 1180708


{{{240}}}, {{{234}}}, {{{78}}}, {{{72}}}

find differences

{{{240}}}........{{{234}}}........{{{78}}}........{{{72}}}
.........{{{-6}}}..........{{{-156}}}........{{{-6}}}.......
.............{{{-150}}}..........{{{150}}}

...................{{{300}}}-> third differences are same, means nth term formula will be



{{{a[n]=an^3+bn^2+cn+d}}}


set up the system

{{{240=a*1^3+b*1^2+c*1+d}}}
{{{240=a+b+c+d}}}.............eq.1

{{{234=a*2^3+b*2^2+c*2+d}}}
{{{234=8a+4b+2c+d}}}.............eq.2

{{{78=a*3^3+b*3^2+c*3+d}}}
{{{78=27a+9b+3c+d}}}.............eq.3

{{{72=a*4^3+b*4^2+c*4+d}}}
{{{72=64a+16b+4c+d}}}.............eq.4

when you solve the system above, you will get

{{{a = 50}}}, {{{b = -375}}}, {{{c = 769}}}, {{{d = -204}}}

and nth term formula is:

{{{a[n]=50n^3-375n^2+769n-204}}}

the next term is {{{a[5]}}}=> {{{n=5}}}

{{{a[5]=50*5^3-375*5^2+769*5-204}}}
{{{a[5]=516}}}


{{{240}}}, {{{234}}}, {{{78}}}, {{{72}}},{{{516}}}