Question

For the AP –3, –7, –11,… can we find directly $a_{30}-a_{20}$ without actually finding $a_{30}and{a}_{20}$? Give the reason for your answer.

Answer 1

Yes, it's possible because the difference between any two terms of an AP is proportional to the common difference of that AP.

So, we can find directly $a_{30}-a_{20}$ without actually finding $a_{30}and{a}_{20}$

Explanation:

Given AP: –3, –7, –11,…

nth term of an AP, $a_n=a+(n-1)d$
$\therefore a_{30}=a+(30-1)d=a+29d$
$and{a}_{20}=a+(20-1)d=a+19d$
$Now,a_{30}-a_{20}=(a+29d)-(a+19d)=10d$

Now we just have to find the common difference, $d=-7-(-3)=-7+3$
$=-4$

$\therefore a_{30}-a_{20}=10(-4)=-40$

Hence, we found directly $a_{30}-a_{20}$ without actually finding $a_{30}and{a}_{20}$.