Question

9. how many sticks are needed for the 91st pattern

Answer 1

EXPLANATION

Let's see the facts:

We have a sequence here as follows:

First pattern: 12 sticks

Second pattern: 19 sticks

Third pattern: 26 sticks

Given the sequence:

12, 19, 26

The nth term is obtained by applying the following formula.

$a_n=a_1+(n-1)d$

Check wheter the difference is constant:

Compute the difference of all the adjacent terms:

$d=a_n-a_{n-1}$

19-12 = 7 , 26-19=7

The difference between all of the adjacent terms is the same and equal to d=7

The first element of the sequence is:

a_1=12

Therefore, the nth term is computed by:

$a_n=12+7(n-1)$

So, when n=91, the number of sticks are:

$a_{91}=12+7(91-1)=12+7(90)=12+630=642$

Thus, there are 642 sticks in the 91st pattern.