Answer:
a) 26 sticks
b) an = 6 +4(n -1)
Explanation:
You have patterns of sticks that have 6 sticks in the first pattern, 10 sticks in the second pattern, 14 sticks in the third pattern, and you want to know the number of sticks in the 6th pattern and in pattern number n.
b) Arithmetic sequence
You have a sequence of patterns with 6, 10, and 14 sticks. The first pattern has 6, and the following patterns each have 4 more than the one previous. The sequence of numbers is an arithmetic sequence with a first term a1=6, and a common difference d=4.
The n-th term of such a sequence is given by the formula ...
an = a1 +d(n -1)
For the first term and common difference in this sequence, the number of sticks in pattern n is ...
an = 6 +4(n -1)
a) Sixth pattern
When n=6, the number of sticks is ...
a6 = 6 +4(6 -1) = 26
There would be 26 sticks in pattern 6.