How do you find the nth term formula 3,8,15,24,... ?

1 Answer
Jun 13, 2016

Answer:

#a(n) = a(n-1) +2*(n+1)+1#

Explanation:

Having the first term of the sequence
#" "#
#a(0) =3 #
#" "#
# a(1) = 3+5 =8#
#" "#
We realized that
#" "#
#a(1)= a(0) + 2*2+1 #

We also have :
#" "#
#a(2) = a(1) + 2*3 +1 = 8 + 7 =15#
#" "#
#a(3) = a(2) + 2*4 +1= 15 +9 =24#

From above we can realize that each term is the sum of the previous
#" "#
term and 2*(sequence coefficient added to 1) and 1
#" "#
So the nth term will be:
#" "#
#a(n) =a(n-1) +2*(n+1)+1#