Question

WORTH 50 POINTS

Here is a pattern made from sticks:
a) How many sticks would be in pattern number 6?
b) How many sticks would be in pattern number n?

Answer 1

32

5n + 2

Explanation:

Pattern 1 has 7 sticks.

Pattern 2 has 12 sticks. 5 sticks were added to pattern 1.

Patterns 3 has 17 sticks. 5 sticks were added to pattern 2.

Each new pattern adds 5 sticks to the previous pattern.

The number of sticks is an arithmetic sequence with first term 7 and common difference 5.

n = 1, a_1 = 7

n = 2, a_2 = 12

n = 3, a_3 = 17

n = 4, a_4 = 22

n = 5, a_5 = 27

n = 6, a_6 = 32

a_n = a_1 + d(n - 1)

a_n = 7 + 5(n - 1)

a_n = 7 + 5n - 5

a_n = 5n + 2