-1

How can I find the largest possible common difference of an arithmetic progression given that its three terms (not necessarily adjacent) are $0.37$, $9$ and $\frac{71}{7}$?

Overdrowsed
  • 51

1 Answers1

1

The common difference must divide the difference of any two terms of an AP. So it must divide $9-0.37=863/100$ and $71/7-9=8/7$. You want the largest common difference, i.e. the HCF of $8.63$ and $8/7$. Now use the following link: Rational Numbers - LCM and HCF.

Shubham Johri
  • 17,659
  • $9 - 0.37 = 863/100$ but by the method you proposed the GCD is pretty small. – Yuki.F Jan 07 '21 at 15:58
  • @Yuki.F Thanks for spotting the error. The difference is indeed small. Did I miss a larger solution? – Shubham Johri Jan 07 '21 at 16:04
  • The answer sheet says $\frac{1}{700}$, which is the HCF of $8.63$ and $\frac{8}{7}$. – Overdrowsed Jan 07 '21 at 16:12
  • 1
    @Dambacha Cool, my answer is correct then. – Shubham Johri Jan 07 '21 at 16:12
  • HCF and LCM of fractions is a concept I've never heard before, though. I'll try and look for a video explanation as I didn't quite understand those given in the linked thread. Thanks for the answer! – Overdrowsed Jan 07 '21 at 16:14
  • @Dambacha You can get in touch with me using the comment option if you have trouble understanding. – Shubham Johri Jan 07 '21 at 16:19
  • Actually I understood the concept thanks to the third solution in the thread you linked by user103816, which was the best and the simplest explanation. Not sure why it isn't the top voted one! – Overdrowsed Jan 07 '21 at 16:25