Question

What is the nth term rule of the quadratic sequence below? 6,12,20,30,42,56,72

Answer 1

The ninth term is 110 beacsue you are adding two every time.

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Answer 2

Answer:

n(squared)^2 + 3n + 4.

Step-by-step explanation:

Sequence: 6, 12, 20, 30, 42, 56, 72.

First, lets find the first difference between the numbers. (In other words, let find the number gap difference between the first, second, third, fourth, fifth, sixth and seventh term).

In this case, it'll be..

first difference = 6.

second difference = 8.

third difference = 10.

fourth difference = 12.

fifth difference = 14.

sixth difference = 16.

Now we have the differences between the numbers, we need to do the second difference, which in this case is 3, meaning you have 3n.

Then, you would find out that n(squared)^2, is gonna be part one of your answer.

So, therefore so far we have in our answer: n^2 + 3n.

To then find the last part of our answer, we find our term 0. (The term before the first one given, in this case is 6).

So then you do you do your Term 1 = 6, and then take 2 away from it, giving you 4.

So, our final answer should be, n^2 + 3n + 4.

Hope :)

-Emilie Xo this is right and it helps! Xo