Answer:
32 and 5n + 2
Step-by-step explanation:
(a)
The pattern of the number of sticks is
7, 12, 17
There is a common difference of 5 between consecutive terms.
Thus to obtain the number of sticks in number 6 , add 5 to previous terms, that is
a₄ = 17 + 5 = 22
a₅ = 22 + 5 = 27
a₆ = 27 + 5 = 32
There are 32 sticks in pattern number 6
(b)
The sequence is arithmetic with n th term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
Where a₁ is the first term and d the common difference
Here a₁ = 7 and d = 5 , then
[tex]a_{n}[/tex] = 7 + 5(n - 1) = 7 + 5n - 5 = 5n + 2
number of sticks in pattern number n is 5n + 2
