Given:
In an arithmetic sequence [tex]b_n[/tex],
[tex]b_1=6,d=3[/tex]
To find:
The value of [tex]b_3[/tex].
Solution:
In an arithmetic sequence [tex]b_n[/tex],
First term : [tex]b_1=6[/tex]
Common difference : [tex]d=3[/tex]
The nth term of an AP is
[tex]a_n=a+(n-1)d[/tex]
For given arithmetic sequence,
[tex]b_n=b_1+(n-1)d[/tex]
Putting [tex]b_1=6,d=3[/tex], we get
[tex]b_n=6+(n-1)3[/tex]
[tex]b_n=6+3n-3[/tex]
[tex]b_n=3+3n[/tex]
Put n=3 to find the values of [tex]b_3[/tex].
[tex]b_3=3+3(3)[/tex]
[tex]b_3=3+9[/tex]
[tex]b_3=12[/tex]
Therefore, the value of [tex]b_3[/tex] is 12.
