Question

The total number of toothpicks also forms a sequence: 4, 12, 24, 40, ... What rule describes this sequence?

a. an=2(n^2+n)
b. an=2n^2
c. an=2(n^2+1)
d. an=(n^2+n)/2

Answer 1

rule describes this sequence is
an = 2 ( n^2 + n )

n = 1

an = 2 ( 1^2 + 1 )
an = 2 ( 1 + 1 )
an = 2 ( 2 )
an = 4

n = 2

an = 2 ( 2^2 + 2 )
an = 2 ( 4 + 2 )
an = 2 ( 6 )
an = 12

n = 3

an = 2 ( 3^2 + 3 )
an = 2 ( 9 + 3 )
an = 2 ( 12 )
an = 24

n = 4

an = 2 ( 4^2 + 4 )
an = 2 ( 16 + 4 )
an = 2 ( 20 )
an = 40