Question

Find n if the given value of x is the nth term of the given A.P.

`1, 21/11, 31/11, 41/11,......, x = 171/11`

Answer 1

`1, 21/11, 31/11, 41/11`

`a_n = 171/11`

Let us take the total number terms as n

So

First term (a) = 1

Last term `(a_n) = 171/11`

Common difference (d) = `21/11 = -1`

`= (21 - 11)/11`

= 10/11

Now, as we know,

`a_n =  a + (n - 1)d`

So, for the last term,

`171/11 = 1 + (n -1)(10/11)`

`171/11 = 1 + 10/11 n - 10/11`

`171/11 = (11 - 10)/11 + 10/11 n`

`171/11 = 1/11 + 10/11 n`

On further simplifying, we get,

`10/11n = 171/11 - 1/11`

`10/11 n = 170/11`

`n = ((170)(11))/((11)(10))`

n = 17

Therefore the total number of term of the given A,P is  n = 17