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Question

The number of terms which are identical in the sequence 2,5,8,11,upto 60 terms and 3,5,7,9,upto 50 terms, is

A
16
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B
19
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C
18
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D
17
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Solution

The correct option is D 17
2,5,8,11,upto 60 terms
T60=2+(601)3=179

3,5,7,9,upto 50 terms
T50=3+(501)2=101

Now, the common difference of first A.P. is 3
and the common difference of second A.P. is 2.
Therefore, the common difference of the A.P. formed by the common terms of both the A.P. =L.C.M.(3,2)=6
The first common term is 5.

Let there be n common terms.
The last term of the A.P. formed by the common terms of both the A.P. should be less than or equal to 101.
i.e., 5+(n1)6101
n17

Hence, the number of common terms in both the A.P. is 17.


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