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Question

If d,a and l denote the common difference, first and last terms respectively, then nth term from the end is ___________ .

A
l+(n1)d
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B
l(n1)d
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C
d(n1)l
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D
d+(n1)l
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Solution

The correct option is B l(n1)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.
Reverse AP=l,ld,...,a
Last term =a , first term =l and common difference = 2nd term - 1st term =ldl=d
Therefore, nth term
= first term + (n-1)(common difference)
=l+(n1)(d)=l(n1)d

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