Answer:
Recursive formula of an arithmetic sequence is given by the expression,
Tn=a+(n−1)d
Where, Tn= nth term
a= First term of the sequence
n= Number of term
d= Common difference
Therefore, number of sticks in the 6th pattern are 32.
And number of sticks in the nth pattern are Tn=5n+2
From the picture attached,
Number of sticks in 1st pattern = 7
Number of sticks in 2nd pattern = 12
Number of sticks in 3rd pattern = 17
Sequence formed is 7, 12, 17..... nth term
This sequence has a common difference of 5 in each successive term so it will be an arithmetic sequence.
Therefore, nth term of the sequence will be,
Tn=a+(n−1)d
Tn=7+(n−1)5
Tn=5n+2
If n=6,
Tn=7+(6−1)5
Tn=7+25
Tn=32
Hope it helps !
Have a great day!