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Question

Find the number of terms common to the two A,P's 3,7,11,.....,407 and 2,9,16,..........,709

A
12
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B
14
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C
25
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D
28
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Solution

The correct option is C 25
The given terms of AP are 3,7,11.........407 and 2,916,......70
Now,
Let mth term at first sequence be same as the nth terms at the second sequence Then tm and tn
3+(m1)×4=2+(n1)7

4m1=n5

4m7n=5+1

4m=7n4

m=7n44

Now, since n is a whole number, so 7m-4 needs to be divisible by 4. So, then, m can be equal to all multiples of 4 till 102 i.e. 4, 8, 12, 16, 20, 24, ......100So, the number of terms common to the 2 APs would be 25.

Hence, the option (C) is correct answer.


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