Question

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

Answer 1

Answer:

a) 26

b) 4n+2

Step-by-step explanation:

From the given figure it is clear that,

Number of sticks in pattern 1 = 6

Number of sticks in pattern 2 = 10

Number of sticks in pattern 3 = 14

Now,

6, 10, 14, ...

It is an AP.

Here, first term = 6

Common difference  = 10 - 6 = 4

nth term of an AP is

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

where, $a_1$ is first term and d is common difference.

So, nth term of given AP is

$a_n=6+(n-1)4$

$a_n=6+4n-4$

$a_n=4n+2$

Now, substitute n=6 in the above equation to find the number of sticks in pattern 6.

$a_n=4(6)+2=24+2=26$

Therefore, the number of sticks in pattern 6 is 26.

Since $a_n=4n+2$, therefore, the number of sticks in pattern n is 4n+2.