How do I get the equation for the 10th, 20th and nth members in the sequence? The sequence is, 1. 1x1; 1 square; 4 matchsticks 2. 2x2; 2 squares; 12 matchsticks 3. 3x3; 9 squares; 24 matchsticks   How do I find the pattern to make the equation to find the 10th, 20th, and nth members of the sequence?

Expert Answers

An illustration of the letter 'A' in a speech bubbles

10x10 square

Each horizontal lines will have 10 matchsticks.

You will have 11 horizontal lines

Therefore you will have 10*11 horizontal matchsticks

Same work with the vertical matchsticks

You will have 11 vertical lines of 10 matchsticks.

therefore you will have 11*10=110 vertical matchsticks.

 

In total you will have 220=2*11*10

 

If you have a 20x20 square. 


Again you will have 21 horizontal lines of 20 matchsticks and 21 vertical lines of 20 matchsticks. Therefore you have 20*21*2 matchsticks in total.

 

Now for a nxn square

we have horizontal n+1 horizontal lines of n matchsticks and n+1 vertical lines  of n matchsticks. In total we have n*(n+1)*2 matchsticks.

 

Therefore the formula is 2n(n+1) matchsticks for a n x n square.

It is matches the result for n=10, n=20 and of course n=1 n=2, n=3.

 

Formula: 2n(n+1)

matchsticks

 

Approved by eNotes Editorial Team

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial