Question

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

`5 1/2, 11, 16 1/2, 22, ......; x = 550`

Answer 1

In the given problem, we need to find the number of terms in an A.P

We are given,

`a_n = 550`

Let us take the total number of terms as n

So,

First term (a) = `5 1/2`

Last term (`a_n`) = 500

Common difference (d) = `11 - 5 1/2`

`= 11 - 11/2`

`= (22 - 11)/2`

`= 11/2`

Now, as we know,

`a_n = a + (n - 1)d`

So for the last term

`550 = 51/2  + (n - 1)(11/2)`

`550 = 11/2 + 11/2 n - 11/2`

`550 = 11/2 n`

`n = 550(2)/11`

On further simplifying, we get,

`n = 1100/11`

n = 100

Therefore, the total number of terms of the given A.P. is `n = 100`