Set A consists of the numbers in the arithmetic sequence 15, 24, 33.... and Set
B consists of the numbers in the arithmetic sequence 21, 27, 33.... What is the
sum of the five smallest numbers common to both sets?
The common difference of sequence A is 6
The common difference of sequence B is 9
Their smallest common number is 33, since we see that's the 3rd number
in each sequence. The sequences will have the next common term when we
have added enough 6's to 33 in A and enough 9's to 33 in B so that the
number of 6's added in A and the number of 9's added in B will be a
multiple of both 6 and 9, or a multiple of 18. Therefore, the sequence
of common terms will have first term 33, and common difference 18, the
LCM of 6 and 9.
So the first five terms of the sequence of numbers common to both sets
is 33, 51, 69, 87, 105. Their sum is 345.
Edwin