Question

Nth term sequences, please may I get some help. 15 p.

Answer 1

`(n+2)^2+6`

Explanation:

Pattern 1 consists of

`3+3* 3+3` small squares (here n = 1 and
`3* 3=(1+2)* (1+2)`).

Pattern 2 consists of

`3+4* 4+3` small squares (here n = 2 and
`4* 4=(2+2)* (2+2)`).

Pattern 3 consists of

`3+5* 5+3` small squares (here n = 3 and
`5* 5=(3+2)* (3+2)`).

Thus, pattern n consists of

`3+(n+2)* (n+2)+3=6+(n+2)^2` small squares.