Question 942808

  the {{{25}}}th term of the arithmetic sequence:{{{26}}}, {{{13}}},{{{ 0}}},{{{ -13}}}.....



 the nth term of the arithmetic sequence:  {{{a[n]=a[1] +(n-1)d}}} where {{{n}}} is number of the term and {{{d}}} is common difference

you have  the arithmetic sequence: {{{26}}}, {{{13}}}, {{{0}}},{{{ -13}}} where {{{a[1]=26}}} and {{{a[2]=13}}}, so the difference {{{d=-13}}}

{{{a[n]=a[1] +(n-1)(-13)}}}...check the third term ( or {{{n=3}}})

{{{a[3]=26 +(3-1)(-13)}}}
{{{a[3]=26 +(2)(-13)}}} 
{{{a[3]=26 -26}}} 
{{{a[3]=0}}}  which is true

so, the {{{25}}}th term will be:

{{{a[n]=a[1] +(n-1)(-13)}}}......plug in {{{n=25}}} and {{{a[1]=26}}}

{{{a[25]=26+(25-1)(-13)}}}

{{{a[25]=26+(24)(-13)}}}

{{{a[25]=26-312}}}

{{{a[25]=-286}}}