Answer:
a) 32
b) 2 +5n
Explanation:
Given the stick patterns shown, with 7, 12, 17 sticks, you want to know (a) the number of sticks in pattern 6, and (b) the number of sticks in pattern n.
Sequence
The numbers of sticks in the patterns shown are ...
7, 12, 17
The differences between these numbers are ...
12 -7 = 5
17 -12 = 5
That is, the first pattern has 7 and the common difference between patterns is 5. This indicates the sequence is arithmetic.
b) General term
The general term of an arithmetic sequence with first term a1 and common difference d is ...
an = a1 +d(n -1)
an = 7 +5(n -1) = 7 +5n -5
an = 5n +2 . . . . . . sticks in pattern n
a) Sixth term
The term when n=6 is ...
a6 = 5·6 +2 = 32 . . . . . . sticks in pattern 6
__
Additional comment
We find it easier to determine sticks in pattern 6 by first determining the formula for pattern n.
<95141404393>