Question

I need help on part b

Answer 1

• a) The pattern 6 has 26 sticks,
• b) The pattern number n has 4n + 2 sticks.

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If we put the number of sticks in a sequence we get:

• 6, 10, 14, ...

As we see the difference of the terms is common and is 4, and the first term is 6. It is therefore an arithmetic progression with:

• a = 6 and
• d = 4

Use the nth term equation:

• a(n) = a + (n - 1)d

Part a)

Substitute n = 6 to find the number of sticks of the 6th term:

• a(6) = 6 + (6 - 1)*4 = 6 + 5*4 = 6 + 20 = 26

Part b)

Find the nth term:

• a(n) = 6 + (n - 1)*4 = 6 + 4n - 4 = 4n + 2