Answer:
The first four terms of the sequence are:
7,17,31 and 49
Step-by-step explanation:
The expression for the number is shown as:
i.e. [tex]a_{n}= 1+2n(n+2)[/tex]
Hence, the first four terms of the sequence are:
First term:
[tex]a_{1}=1+2\times 1\times(1+2)[/tex]
[tex]a_{1}=1+2\times3[/tex]
[tex]a_{1}=7[/tex]
Second Term:
[tex]a_{2}=1+2\times2\times(2+2)\\\\a_{2}=1+16\\\\a_{2}=17[/tex]
Third Term:
[tex]a_{3}=1+2\times3\times(3+2)\\\\a_{3}=1+30\\\\a_{3}=31[/tex]
Fourth Term:
[tex]a_{4}=1+2\times4\times(4+2)\\\\a_{4}=1+48\\\\a_{4}=49[/tex]
Hence , the first four terms of the sequence are :
[tex]a_{1}=7[/tex]
[tex]a_{2}=17[/tex]
[tex]a_{3}=31[/tex]
[tex]a_{4}=49[/tex]
