Question

The expression 1+2n(n+2) describes a pattern of numbers, where n represents a numbers position in the sequence. Write the first four terms of the sequence

Answer 1

The first four terms of the sequence are:

7,17,31 and 49

Explanation:

The expression for the number is shown as:

i.e.
`a_(n)= 1+2n(n+2)`

Hence, the first four terms of the sequence are:

First term:

`a_(1)=1+2* 1*(1+2)`

`a_(1)=1+2*3`

`a_(1)=7`

Second Term:

`a_(2)=1+2*2*(2+2)\\\\a_(2)=1+16\\\\a_(2)=17`

Third Term:

`a_(3)=1+2*3*(3+2)\\\\a_(3)=1+30\\\\a_(3)=31`

Fourth Term:

`a_(4)=1+2*4*(4+2)\\\\a_(4)=1+48\\\\a_(4)=49`

Hence , the first four terms of the sequence are :

`a_(1)=7`

`a_(2)=17`

`a_(3)=31`

`a_(4)=49`