Question

Question 3
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

True.
nth term of an AP, $a_n=a+(n-1)d$
$\therefore a_{30}=a+(30-1)d=a+29d$
$and{a}_{20}=a+(20-1)d=a+19d$
$Now,a_{30}-a_{20}=(a+29d)-(a+19d)=10d$
Common difference, d = -7 - (-3) = -7 + 3
= - 4
$\therefore a_{30}-a_{20}=10(-4)=-40$