Question
Download Solution PDFLet an and bn be two sequences such that an = 13 + 6(n - 1) and bn = 15 + 7(n - 1) for all natural numbers n. Then, the largest three digit integer that is common to both these sequences, is
Answer (Detailed Solution Below) 967
Detailed Solution
Download Solution PDF{an} = {13, 19, 25, 31, 37, 43, 49,...}
{bn} = {15, 22, 29, 36, 43, 50, ......}
First common term = 43
Any next common term can be found out by using = 43 + LCM (6, 7)K = 43 + 42K
where K is a positive integer.
For K = 22, 43 + 42K = 967
Hence, the largest three digit number common to both these sequence is 967.