Turn on thread page Beta
 You are Here: Home >< Maths

# Quick un, proof by induction watch

1. Hey

Show that f(k+1) - f(k) is divisible by 15.

f(n) = 3^4n + 2^4n+2

b) Prove that f(n) is divisible by 5

Check for 1, assume for K etc.

3^4(k+1) + 2^(4(k+1)+2) - (3^4k + 2^4k+2)
= 3^(4k + 4) + 2^(4k+6) - (3^4k + 2^4k+2)
= 81.3^4k + 16.2^(4k+2) - (3^4k + 2^4k+2)
= 80.3^4k + 15.2^4k+2

80 isn't divisible by 15. Stuck.

and for part be, how do you show that it's divisible by 5? You know it's divisible by 15 which is 5 multiplied by 3 hence divisible by 5 but how do you show that?

Many Thanks!
2. 80 x 3^(4k) = 16 x 5 x 3^(4k) = 16 x 15 x 3^(4k-1)
3. (Original post by Glutamic Acid)
80 x 3^(4k) = 16 x 5 x 3^(4k) = 16 x 15 x 3^(4k-1)
Aha, that is sneaky! Thanks!

Turn on thread page Beta
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: January 31, 2010
Today on TSR

Uni realities

### University open days

• University of Lincoln
Mini Open Day at the Brayford Campus Undergraduate
Wed, 19 Dec '18
• University of East Anglia
UEA Mini Open Day Undergraduate
Fri, 4 Jan '19
• Bournemouth University
Wed, 9 Jan '19
Poll
Useful resources

## Make your revision easier

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

Can you help? Study help unanswered threads

## Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE