Question

Write a rule for the nth term of the arithmetic sequence:

a11= 50, d = 7

Answer 1

Required rule for
`n^(th)` is
`a_(n)=7n-27`.

Explanation:

Given that,

`a_(11) = 50,\ \ d=7`

From the question: we have to write the
`n^(th)` term of Arithmetic sequence.

Arithmetic Sequence or Arithmetic progression (A.P) : It is a sequence which possess that difference between of two successive sequence is always constant.

`a_(1) ,a_(2),a_(3),a_(4).....................a_(n-1),a_(n)`

where,
`a_(1)` is the first term of A.P

`d` is the common difference.

`a_(n)` is the last term or general term.

The above sequence to be in A.P then their common difference should be equal.

`d=a_(2)-a_(1) =a_(3)-a_(2)=a_(4) -a_(3) ..........................a_(n)-a_(n-1)`

Now, Formula of General Term is
`a_(n)=a+(n-1)d`

So,
`a_(11)= a+(11-1)d\\ a_(11) = a+10d`

Substituting the value of
`a_(11) = 50,\ \ d=7` we get,

`50=a+10*7\\50=a+70\\a=-20`

Then General term (
`a_(n)`) of given data is

`a_(n)=-20+(n-1)7\\a_(n)=-20+7n-7\\a_(n)=7n-27`

Therefore, Required rule for
`n^(th)` is
`a_(n)=7n-27`.