Question

The first and last term of an A.P are 1 and 121 respectively .find the number of terms in an A.P and find the common difference between them if the sum of its term is 1281

Answer 1

Answer:

Number of terms = 21

Common difference = 6

See the attachment...

Answer 2

The number of terms in an A.P is 21

The common difference between them is 6

Step-by-step explanation:

As given in question, the first and last term of an A.P are 1 and 121 respectively

And the sum of its term is 1281

Let the first terms is a

Let the last term is L

Let the common difference is d

As we know that the sum of given term A.P. is given by

$\Rightarrow S=\frac{n}{2}\times\left ( a+L \right )$

$\Rightarrow 1281=\frac{n}{2}\times\left ( 1+121 \right )$

$\Rightarrow 1281 \times 2=n\times\left ( 122 \right )$

$\Rightarrow n=\frac{1281 \times2}{122}$

$\Rightarrow n=21$

For finding the d we use,

$\Rightarrow A ( n )=L= a+( n-1 )d$

$\Rightarrow 121= 1+( 21-1 )d$

$\Rightarrow d=\frac{120}{20}$

$\Rightarrow d=6$

The number of terms in an A.P is 21

The common difference between them is 6