+0  
 
0
26
1
avatar

An arithmetic sequence with first term 1 has a common difference of 6. A second sequence begins with 4 and has a common difference of 7. In the range of 1 to 100, what is the largest number common to both sequences?

 
Guest Aug 9, 2018
 #1
avatar+26817 
+1

"An arithmetic sequence with first term 1 has a common difference of 6. A second sequence begins with 4 and has a common difference of 7. In the range of 1 to 100, what is the largest number common to both sequences?"

 

We must have:

 

1 + 6n = 4 + 7m    where m and n are integers

 

This can be rearranged as:

6n - 7m = 3  or

2n - 7m/3 = 1

 

m must be a multiple of 3, and, because 2n is always even, 7m/3 must be odd to give a difference of 1.  This means m must be an odd multiple of 3.

 

m           n           2n-7m/3          4+7m          1+6n

3            4               1                    25               25

9            11             1                    67               67

15          18             1                  109             109

 

So 67 is the largest number in the range 1 to 100 that is common to both sequences.

 
Alan  Aug 9, 2018

13 Online Users

avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.