Question

Write a rule for the nth term of the arithmetic sequence: a11= 50, d = 7

Answer 1

Answer:

Required rule for $n^{th}$ is $a_{n}=7n-27$.

Step-by-step 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,

                                                         $50=a+10\times7\\50=a+70\\a=-20$

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 $a_{n}=7n-27$.