Question
Write the expression of the common difference of an A.P. whose first term is a and $n^{th}$ term is b.
✓
Answer
Here, we are given
First term $= a$
Last term $= b$
Let us take the common difference as $d$
Now, we know
$a_n = a + (n - 1)d$
So,
For the last term $(a_n),$
$b = a + (n - 1)d$
$b - a = (n - 1)d$
$\text{d}=\frac{\text{b}-\text{a}}{\text{n}-1}$
Therefore, common difference of the A.P. is $\text{d}=\frac{\text{b}-\text{a}}{\text{n}-1}$.
First term $= a$
Last term $= b$
Let us take the common difference as $d$
Now, we know
$a_n = a + (n - 1)d$
So,
For the last term $(a_n),$
$b = a + (n - 1)d$
$b - a = (n - 1)d$
$\text{d}=\frac{\text{b}-\text{a}}{\text{n}-1}$
Therefore, common difference of the A.P. is $\text{d}=\frac{\text{b}-\text{a}}{\text{n}-1}$.
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