Question 711986


as you can see, in the following arithmetic sequence, {{{315}}}, {{{304}}}, {{{293}}}, ... , {{{18}}}, the difference between each term is {{{-11}}} (the fixed amount is called the common difference, {{{d=a[2]-a[1]=304-3115=-11}}})

{{{315}}}

{{{315-11=304}}}

{{{304-11=293}}}...then next term will be

{{{293-11=282}}}

{{{282-11=271}}}....and so on, up to {{{18}}}


To find any term of an arithmetic sequence use formula: 

{{{a[n]=a[1]+(n-1)d}}} where {{{a[1]}}} is the first term of the sequence,
{{{d}}} is the common difference, {{{n}}} is the number of the term to find

in your case is given {{{a[1]=315}}},{{{a[n]=18}}}, and we found that {{{d=-11}}}

{{{a[n]=a[1]+(n-1)d}}}...solve for {{{n}}}

{{{a[n]-a[1]=(n-1)d}}}

{{{(a[n]-a[1])/d=n-1}}}

{{{(a[n]-a[1])/d+1=n}}}......plug in given values

{{{(18-315)/-11+1=n}}}

{{{(18-315)/-11+1=n}}}

{{{-297/-11+1=n}}}

{{{27+1=n}}}

{{{28=n}}}......the number of terms