Question

If $d,a$ and $l$ denote the common difference, first and last terms respectively, then $n^{th}$ term from the end is ___________ .

• A. $l+(n-1)d$
• B. $d-(n-1)l$
• C. $l-(n-1)d$
• D. $d+(n-1)l$

Answer 1

The correct option is C $l-(n-1)d$

Given, first term = a , common difference = d and last term = l.
Corresponding $AP=a,a+d,...,l$
Now, reverse the AP, we again get an AP.
$ReverseAP=l,l-d,...,a$
Last term $=a$ , first term $=l$ and common difference = 2nd term - 1st term $=l-d-l=-d$
Therefore, nth term
= first term + (n-1)(common difference)
$=l+(n-1)(-d)=l-(n-1)d$