Respuesta :
Answer:
Required rule for [tex]n^{th}[/tex] is [tex]a_{n}=7n-27[/tex].
Step-by-step explanation:
Given that,
[tex]a_{11} = 50,\ \ d=7[/tex]
From the question: we have to write the [tex]n^{th}[/tex] 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.
[tex]a_{1} ,a_{2},a_{3},a_{4}.....................a_{n-1},a_{n}[/tex]
where, [tex]a_{1}[/tex] is the first term of A.P
[tex]d[/tex] is the common difference.
[tex]a_{n}[/tex] is the last term or general term.
The above sequence to be in A.P then their common difference should be equal.
[tex]d=a_{2}-a_{1} =a_{3}-a_{2}=a_{4} -a_{3} ..........................a_{n}-a_{n-1}[/tex]
Now, Formula of General Term is [tex]a_{n}=a+(n-1)d[/tex]
So, [tex]a_{11}= a+(11-1)d\\ a_{11} = a+10d[/tex]
Substituting the value of [tex]a_{11} = 50,\ \ d=7[/tex] we get,
[tex]50=a+10\times7\\50=a+70\\a=-20[/tex]
Then General term ([tex]a_{n}[/tex]) of given data is
[tex]a_{n}=-20+(n-1)7\\a_{n}=-20+7n-7\\a_{n}=7n-27[/tex]
Therefore, Required rule for [tex]n^{th}[/tex] is [tex]a_{n}=7n-27[/tex].
