What is the rule for this pattern? 3,9,18,30,45

Question

My teacher gave me this number pattern and said find the rule. he didn't even know so what is the rule for this number pattern? 3,9,18,30,45. I do want to know how in the easiest way.

Answer 1

It is a quadratic pattern as 3 to 9 is 6 and 9 to 18 is 9 and 18 to 30 is 12. The 2nd difference is 3. Therefore use the general term formula for quadratic patterns to determine the rule ;)

Answer 2

3*n(n+1)/2

Answer 3

(3n+3n^2)/2

Answer 4

It's the number of extra dots each time you add a number to a set of dominoes!

Answer 5

It's plus the table of three so first it's +6 then it's +9, +12, +15, +18 and so on.

Answer 6

for nth term, n--> 3n(n+1)/2

It's the number of lines connecting nodes to make up a triangular lattice.

Answer 7

The numbers 3, 6, 9, 12, 18, 30, .... are according to the quadratic pattern:
f(n) = (1/2)n^2 + (3/2)n
we can continue the sequence by substituting values for n and calculating the corresponding terms.

3, 6, 9, 12, 18, 30, 35, 44, 54, ...