Find the recursive quadratic formula of the sequence: 1, 3, 7, 13, 21

The sequence

1, 3, 7, 13, 21, ...

has first-order differences

2, 4, 6, 8, ...

Let denote the original sequence, and the sequence of first-order differences. It's quite clear that

for . By definition of first-order differences, we have

for , or

By substitution, we have

and so on, down to

You should know that

and we're given , so

or

Alternatively, since we already know the sequence is supposed to be quadratic, we can look for coefficients such that

We have

and we can solve this system for the 3 unknowns to find .

option: d is the correct answer.

d) none of the above.

step-by-step explanation:

clearly from the figure attached to the question we could see that there is no shape given. hence without any shape given in the figure and after rotation we can't obtained a square pyramid.

since, to obtain a image we need a proper figure of the pre-image so that it can be transformed.

hence, the correct answer is:

d) none of the above.

step-by-step explanation: