Patterns and Sequences Stage 4 - Short Problems

A collection of short Stage 4 problems on patterns and sequences



Producing an Integer

Stage: 3 and 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?

Fibonacci Deduction

Stage: 3 and 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?

Big Fibonacci

Stage: 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

Stage: 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

Stage: 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?

Lumber9

Stage: 3 Short Challenge Level: Challenge Level:1

Weekly Problem 30 - 2016
The base of a pyramid has n edges. What is the difference between the number of edges of the pyramid and the number of faces?