i. How many small squares are there in each rectangle? ii. How many large squares?

Question

See the pictures below:

i. How many small squares are there in each rectangle?

ii. How many large squares?

iii. How many squares in all? Continuing this pattern, is each such sequence of numbers, an arithmetic sequence?

Answer 1

i. No., of small squares in the first picture = 2

No. of small squares in the second picture = 4

No. of small squares in the third picture = 6

No. of small squares in the fourth picture = 8

ii. No. of big squares in first picture = 0 

No. of big squares in second picture = 1 

No. of big squares in third picture = 2 

No. of big squares in fourth picture = 3

iii. Total squares in first picture = 2 

Total squares in second picture = 5 

Total squares in third picture = 8 

Total squares in fourth picture = 11 

Sequence of no. of small squares 2, 4, 6, 8 

This is an arithmetic sequence with common difference = 2 

Sequence of no. of big squares, 0, 1, 2, 3

This is an arithmetic sequence with common difference = 1

Sequence of Total no. of squares 2, 5, 8, 11 

This is an arithmetic sequence with common difference = 3