Question

find the nth term of this quadratic sequence 3, 11, 25, 45 mathswatch please help i never know how to find the n^2 sequences

Answer 1

Answer:

Below.

Step-by-step explanation:

Let n be the sequence number of a term:

n:                   1       2       3       4

Term:            3      11      25     45

Differences:      8      14      20

Differences:          6       6              <- the 6 indicates a 3n^2.

3n^2:            3      12      27     48

Subtract

from Term:   0       -1       -2      -3

The last row is an Arithmetic sequence with  first term 0 and common difference -1, so the nth term is

3n^2 + 0 + (n - 1)*-1

= 3n^2 - n + 1       (Answer).