Question

Write the expression for the common difference of an$A.P$ whose first term is $a$ and $nth$ term is $b$.

Answer 1

We have,

first term $A=a$

Common difference $D=?$

And $n^{th}$ term $A_n=b$

Then,

We know that,

$A_n=A+(n-1)D$

$\Rightarrow b=a+(n-1)D$

$\Rightarrow (b-a)=(n-1)D$

$\Rightarrow D=\frac{(b-a)}{(n-1)}$

Hence, this is the answer.