Quadratic Sequence help.?

Question

Hey. I was wondering if someone could please help me as i am having difficulties with quadratic sequences.

1.The sequence is 1, 4, 13, 40, 121...

2. The sequence is 2, 5, 10, 17, 26...

I was wondering could you please tell me how to solve these. Is there a formula? All comments are very much appreciated. Many thanks!

Answer 1

1.Using equations

1=(a*(1^2))+(b*1)+c

4=(a*(2^2))+(b*2)+c

13=(a*(3^2))+(b*3)+c

and using a program on internet, I get

a=3, b=-6, and c=4 or

y=3x^2-6x+4

2. Using

2=(a*(1)^2))+(b*1)+c

5=(a*(2)^2)+(b*2)+c

10=(a*(3)^2)+(b*3)+c I get

a=1, b=0, c=1 or

y=x^2+1

Answer 2

(1) formula=x+3^n where n=1,2,3,...; x=1,4,13,40,121,...

eg: 1+3^1=4

4+3^2=13

13+3^3=40

40+3^4=121

(2) Just add odd number(3,5,7,9,11,13,...) to the previous number.

eg: 2+3=5

5+5=10

10+7=17

17+9=26