Question

The number of terms common to three A.Ps each having 500 terms with first terms 1, 2 and 3: and common
differences 2, 3 and 4 respectively, is equal to:

Answer 1

Step-by-step explanation:

First A.P

′

s sequence is 3,7,11,....,407

General term will be 4k+3 k≤101

Second A.P

′

s sequence is 2,9,16,....,709

General term will be 7p+2 p≤101

The common terms will be 51,79,...,28m+51

28m+51≤407⟹28k≤356⟹k≤12.71

And adding the 2 starting number count of the 2 A.P

′

s i.e. 3 & 2

Number of common terms will be 12+2=14