Question

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

−1, −3, −5, −7, ...; x = −151

Answer 1

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

-1, -3, -5, -7 …

We are given,

`a_n = -151`

Let us take the total number of terms as n.

So,

First term (a) = −1

Last term (a_n) = −151

Common difference (d) = -3 - (-1)

= -3 + 1

= -2

Now as we know

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

SO for the last term

`-151 = -1 + (n - 1)(-2)`

-151 = -1 - 2n + 2

-151 =  - 2n

-2n = 151 - 1

On further simplifying, we get,

-2n = -152

`n = (-152)/(-2)`

n = 76

Therefore, the total number of terms of the given A.P. is n = 76