Question

the first term of an AP is 45 and the sum is 400. Find the number of terms and common difference

Answer 1

S O L U T I O N : (Ques.Error)

$\bf{\large{\underline{\bf{Given\::}}}}}$

• The first term of an A.P. = 5
• The last term of an A.P. = 45
• The sum = 400

$\bf{\large{\underline{\bf{To\:find\::}}}}}$

The number of terms and common difference.

$\bf{\large{\underline{\bf{Explanation\::}}}}}$

We know that formula of the last term of the sum of an A.P;

$\boxed{\bf{S_n=\frac{n}{2} \bigg(a+l\bigg)}}}}$

A/q

$\longrightarrow\tt{400=\dfrac{n}{2} \bigg(5+45\bigg)}\\\\\longrightarrow\tt{800=n(50)}\\\\\longrightarrow\tt{800=50n}\\\\\longrightarrow\tt{n=\cancel{800/50}}\\\\\longrightarrow\bf{n=16}$

We know that formula of the A.P;

$\boxed{\bf{a_n=a+(n-1)d}}}}$

$\longrightarrow\tt{5+(16-1)d=45}\\\\\longrightarrow\tt{5+15d=45}\\\\\longrightarrow\tt{15d=45-5}\\\\\longrightarrow\tt{15d=40}\\\\\longrightarrow\tt{d=\cancel{40/15}}\\\\\longrightarrow\bf{d=8/3}$

Thus;

The number of terms & common difference will be 16 & 8/3 .