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Question

For the AP –3, –7, –11,… can we find directly a30a20 without actually finding a30 and a20? Give the reason for your answer.

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Solution

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 a30a20 without actually finding a30 and a20

Explanation:

Given AP: –3, –7, –11,…

nth term of an AP, an=a+(n1)d
a30=a+(301)d=a+29d
and a20=a+(201)d=a+19d
Now, a30a20=(a+29d)(a+19d)=10d

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

a30a20=10(4)=40

Hence, we found directly a30a20 without actually finding a30 and a20.


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