Question

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

(i) 25, 50, 75, 100, ...; x = 1000

(ii) −1, −3, −5, −7, ...; x = −151

(iii) $5\frac{1}{2},11,16\frac{1}{2},22,...;x=550$

(iv) $1,\frac{21}{11},\frac{31}{11},\frac{41}{11},...,x=\frac{171}{11}$

Answer 1

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

(i) 25, 50, 75, 100 …

We are given,

Let us take the total number of terms as n.

So,

First term (a) = 25

Last term (a_n) = 1000

Common difference (d) =

Now, as we know,

So, for the last term,

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

(ii) -1, -3, -5, -7 …

We are given,

Let us take the total number of terms as n.

So,

First term (a) = −1

Last term (a_n) = −151

Common difference (d) =

Now, as we know,

So, for the last term,

On further simplifying, we get,

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

(iii)

We are given,

Let us take the total number of terms as n.

So,

First term (a) =

Last term (a_n) = 550

Common difference (d) =

Now, as we know,

So, for the last term,

On further simplifying, we get,

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

_(iv)

We are given,

Let us take the total number of terms as n.

So,

First term (a) = 1

Last term (a_n) =

Common difference (d) =

Now, as we know,

So, for the last term,

On further simplifying, we get,

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