Question

In an ap if kth term is l ,lth term is k ,l is not equal to k find nth term​

Answer 1

The nth term​ of the A.P is $a_{n}$ =  K + I - n

Given that;

kth term i.e. $a_{k}$ = I and lth term i.e. $a_{I}$ = K

To find;

The nth term​ of the A.P

Solution;

We know that the general term of an A.P is given by,

$a_{n}$ = a + (n -1)d  where n = Number of terms, a = first term and d = common difference .

According to question we have,

$a_{k}$ = I  i.e.

a + (k - 1)d = I...(1) and,

$a_{I}$ = K  i.e.

a + (I - 1)d = k...(2)

Subtracting (1) from (2) we get,

K - I = a - a + (I -1)d - (k -1)d

K - I =  - d( K - I)

d = - 1

Putting the value of d = - 1 in equation (1) and (2)  we get,

a + (k - 1)( - 1) = a - K + 1

a + (I - 1)( - 1) = a -I + 1

Adding both the equations we get,

$a_{k}$ +  $a_{I}$ = 2a - K - I + 2

2(K + I) = 2a + 2

a = K + I - 1 (First term of an A.P)

Therefore, the nth term of an A.P is given by,

$a_{n}$ = a + (n - 1)d

$a_{n}$ =  K + I - 1 - n + 1

$a_{n}$ =  K + I - n

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Answer 2

Answer:the nth term of an A.P is given by  K + I - n

Step-by-step explanation:

The nth term​ of the A.P is  =  K + I - n

Given that;

kth term i.e.  = I and lth term i.e.  = K

To find;

The nth term​ of the A.P

Solution;

We know that the general term of an A.P is given by,

= a + (n -1)d  where n = Number of terms, a = first term and d = common difference .

According to question we have,

= I  that is:-

a + (k - 1)d = I...(1) and,

= K  that it

a + (I - 1)d = k...(2)

Subtracting (1) from (2) we get,

K - I = a - a + (I -1)d - (k -1)d

K - I =  - d( K - I)

d = - 1

Putting the value of d = - 1 in equation (1) and (2)  we get,

a + (k - 1)( - 1) = a - K + 1

a + (I - 1)( - 1) = a -I + 1

Adding both the equations we get,

+   = 2a - K - I + 2

2(K + I) = 2a + 2

a = K + I - 1 (First term of an A.P)

Therefore, the nth term of an A.P is given by,

= a + (n -1)d equals

=  K + I - 1 - n + 1

=  K + I - n

Answer:-the nth term of an A.P is given by  K + I - n

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