Question

The first five terms in a quadratic sequence are shown below.

5, 14, 29, 50, 77,...
What is the nth term in the sequence?
A. 4n2 + 2
B. 3n2 + 3
C. 3n2 + 2
D. 2n2 + 3

Answer 1

So take the first term i.e 5, and the second term is 14

Answer 2

for first term n=1 and for second term n=2

Answer 3

as you see the options are in the for an^2 + c where the values of a and c are changing

Answer 4

so for n = 1, the quadratic will be a*1^2 + c = a+c
for n=2, it will be a*2^2 + c = 4a+c

Answer 5

we know a+c = 5 (1st term)
and 4a+c = 14 (2nd term)

Answer 6

So if we subtract the first term from 2nd term then we get
(4a+c) - (a+c) = 14 - 5
So 3a = 9

Answer 7

Now you can find the value of a
once you get use the value of "a" and substitute in the equation a+c = 5 to get the value of c

Answer 8

Now see which option satisfies

Answer 9

It would be B wouldn't it..

Answer 10

Nope but you are partially correct,

Answer 11

the 3n^2 part is correct. Did you get what I said earlier?

Answer 12

I honestly understand now. Thank you so much for your help, now that you explained it better then my teacher, I now understand this.

Answer 13

Haha thanks,so what is the answer?

Answer 14

C

Answer 15

great!

Answer 16

Haha Thanks a billion!