Patterns and Sequences Stage 4 - Short Problems


This is part of our collection of Short Problems.

You may also be interested in our longer problems on Patterns and Sequences - Stage 4.

Below 400

KS 3 & 4 Short Challenge Level:

Challenge Level:1

Weekly Problem 51 - 2006
Can you work out which number will appear directly below 400 in this pattern?

Fibonacci Deduction

KS 3 & 4 Short Challenge Level:

Challenge Level:1

Weekly Problem 52 - 2010
Leonard writes down a sequence of numbers. Can you find a formula to predict the seventh number in his sequence?

Producing an Integer

KS 3 & 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 46 - 2011
Multiply a sequence of n terms together. Can you work out when this product is equal to an integer?

Big Fibonacci

KS 4 Short Challenge Level:

Challenge Level:1

Weekly Problem 41 - 2012
The fifth term of a Fibbonaci sequence is 2004. If all the terms are positive integers, what is the largest possible first term?

In One... and the Other

KS 4 Short Challenge Level:

Challenge Level:1

Weekly Problem 44 - 2012
Consider two arithmetic sequences: 1998, 2005, 2012,... and 1996, 2005, 2014,... Which numbers will appear in both?

Collatz 13

KS 4 Short Challenge Level:

Challenge Level:1

Weekly Problem 46 - 2012
If a number is even, halve it; if odd, treble it and add 1. If a sequence starts at 13, what will be the value of the 2008th term?