# 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.

Printable worksheets containing selections of these problems are available here:

 Stage 4 ★ Sheet 1 Solutions

### What a Coincidence!

##### KS 4 Short Challenge Level:

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:

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?

### Collatz-ish

##### KS 4 Short Challenge Level:

Weekly Problem 35 - 2014
A sequence is generated using these rules. For which values of n is the nth term equal to n?

### Below 400

##### KS 4 Short Challenge Level:

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

### Alternating Sum

##### KS 4 Short Challenge Level:

Weekly Problem 1 - 2008
Given that the number 2008 is the correct answer to a sum, can you find n?

### Fibonacci Deduction

##### KS 4 Short Challenge Level:

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

##### KS 4 Short Challenge Level:

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?

### Doubly Consecutive Sums

##### KS 4 Short Challenge Level:

Weekly Problem 51 - 2017
How many numbers less than 2017 are both the sum of two consecutive integers and the sum of five consecutive integers?

### Diagonals

##### KS 4 Short Challenge Level:

How many diagonals does a regular icosagon (20 sides) have?

### Difference Sequence

##### KS 4 Short Challenge Level:

When will 2000 appear in this sequence?