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Question

Two A.P's have the same common difference. The first term of these is 3, and that of the other is 8. What is the difference between their
(i) 2nd (ii) 4th (iii) 10th (iv) 30th terms respectively

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Solution

Let the common difference of the two A.P's be d. Then, their nth terms are
an=3+(n1)d and bn=8+(n1)d ........tn=a+(n1)d

anbn=[3+(n1)d][8+(n1)d]

anbn=5 for all nN.

Hence, a2b2=5,a4b4=5,a10b10=5 and a30b30=5.

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