Q.

The number of terms common to two A.P.s 3, 7, 11, …,  407 and 2, 9, 16, …, 709 is

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a

21

b

28

c

14

d

None of these

answer is C.

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Detailed Solution

By inspection, first common term to both the series is 23. Second common term = 51.Third = 79 and so on. These numbers form an A.P.  23, 51, 79, … Since T15=23+14(28)=23+392=415>407 And T14=23+13(28)=387<407 ∴number of common terms = 14.
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The number of terms common to two A.P.s 3, 7, 11, …,  407 and 2, 9, 16, …, 709 is