For the AP ` -3, -7, -11, …` can we find directly `a_(30)-a_(20)` without actually finding `a_(30)` and `a_(20)` ? Give reason for your answer.

Explanation

True
` :' ` n th term of an AP, `a_(n)=a+(n-1)d`
` 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`
and from given AP common difference, `d= -7-(-3)= -7+3= -4`
`:. a_(30)-a_(20)=10(-4)= -40 " " ` [from Eq. (i)]