Question

Q. 11. The fourth term of an A.P. is 11. The sum of the
fifth and seventh terms of the A.P. is 34. Find the
common difference.​

Answer 1

Step-by-step explanation:

hope it helps...........

Answer 2

AnswEr :

$\bf{\Large{\underline{\sf{Given\::}}}}$

The fourth term of an A.P. is 11. The sum of the fifth and seventh term of the A.P. is 34.

$\bf{\Large{\underline{\sf{To\:find\::}}}}$

The common difference.

$\bf{\Large{\underline{\tt{\red{Explanation\::}}}}}$

Let the first term be a and common difference be d.

The 4th term of an A.P. is 11.

$\bf{\Large{\boxed{\sf{a_{n}=a+(n-1)d}}}}}$

A/q

$\implies\sf{a_{4}=11}\\\\\\\implies\sf{a+(4-1)d=11}\\\\\\\implies\sf{\red{a+3d=11.......................(1)}}$

Now,

The sum of the fifth term and seventh term of the A.P. we get;

$\implies\sf{a_{5}+a_{7}=34}\\\\\\\implies\sf{(a+4d)+(a+6d)=34}\\\\\\\implies\sf{a+4d+a+6d=34}\\\\\\\implies\sf{2a+10d=34}\\\\\\\implies\sf{2(a+5d)=34}\\\\\\\implies\sf{a+5d=\cancel{\dfrac{34}{2} }}\\\\\\\implies\sf{\red{a+5d=17........................(2)}}$

Subtracting equation from (1) and (2), we get;

$\implies\sf{a+3d-a-5d=11-17}\\\\\\\implies\sf{-2d=-6}\\\\\\\implies\sf{d\:=\:\cancel{\dfrac{-6}{-2} }}\\\\\\\implies\sf{\red{d\:=\:3}}$

Thus,

The common difference of an A.P. is 3 .