Answer:
a) 22 dots
b) 51 squares
c) Number of dots = 4 + 2 x (number of squares - 1)
Explanation:
Actually, in this question you are better off solving c) first for the formula and then using it to solve a) and b)
Let's look at the relationship between squares and dots:
Number of squares Number of dots
1 4
2 6
3 8
You can see that as the number of squares increases by 1, the number of dots increases by 2 with 4 dots as the starting point
We can easily come up with a formula by treating this as an arithmetic sequence.
The number of dots represents the term # and the number of dots the actual term value
The difference between consecutive terms is 2 and is called the common difference (d)
The nth term will be referred to using aₙ
So we have
a₁ = 4
a₂ = 6
a₃ = 8
The nth term of any arithmetic sequence is
aₙ = a₁ + d(n-1) where d is the common difference
This is the answer to c). Translating to dots and squares we get
Number of dots = 4 + 2 x (number of squares - 1)
a) Use the formula
a₁₀ = 4 + 2(10-1) = 4 + 2 x9 = 4 + 18 = 22 dots
b) Here we are given the value of term = 104
Substituting we get
104 = 4 + 2(n-1)
104-4 = 2(n-1)
100 = 2(n-1)
n-1 = 100/2 = 50
n = 51
That means the there are 51 squares in the diagram which has 104 dots