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
[tex]a_n=a_1+(n-1)d[/tex]
where, [tex]a_1[/tex] is first term and d is common difference.
So, nth term of given AP is
[tex]a_n=6+(n-1)4[/tex]
[tex]a_n=6+4n-4[/tex]
[tex]a_n=4n+2[/tex]
Now, substitute n=6 in the above equation to find the number of sticks in pattern 6.
[tex]a_n=4(6)+2=24+2=26[/tex]
Therefore, the number of sticks in pattern 6 is 26.
Since [tex]a_n=4n+2[/tex], therefore, the number of sticks in pattern n is 4n+2.
