Given:
The nth term of a number sequence is [tex]n^2+2n[/tex].
To find:
The first 3 terms and the 10th term.
Solution:
We have, nth term of a number sequence.
[tex]a_n=n^2+2n[/tex]
For n=1,
[tex]a_1=(1)^2+2(1)[/tex]
[tex]a_1=1+2[/tex]
[tex]a_1=3[/tex]
For n=2,
[tex]a_2=(2)^2+2(2)[/tex]
[tex]a_2=4+4[/tex]
[tex]a_2=8[/tex]
For n=3,
[tex]a_3=(3)^2+2(3)[/tex]
[tex]a_3=9+6[/tex]
[tex]a_3=15[/tex]
For n=10,
[tex]a_{10}=(10)^2+2(10)[/tex]
[tex]a_{10}=100+20[/tex]
[tex]a_{10}=120[/tex]
Therefore, the first three terms are 3, 8 and 15 respectively. The 10th term is 120.
