Given:
The arithmetic sequence is:
[tex]1, 6, 11, 16, 21,...[/tex]
To find:
1. The rule for the nth term of the given arithmetic sequence.
2. The 10th term of the given arithmetic sequence.
Solution:
1. We have,
[tex]1, 6, 11, 16, 21,...[/tex]
Here, the first term is 1 and the common difference is:
[tex]d=a_2-a_1[/tex]
[tex]d=6-1[/tex]
[tex]d=5[/tex]
The nth term of an arithmetic sequence is:
[tex]a_n=a+(n-1)d[/tex]
Where, a is the first term and d is the common difference.
Putting [tex]a=1,\ d=5[/tex], we get
[tex]a_n=1+(n-1)5[/tex]
[tex]a_n=1+5n-5[/tex]
[tex]a_n=5n-4[/tex]
Therefore, the nth term of the given sequence is [tex]a_n=5n-4[/tex].
2. We need to find the 10th term of the given arithmetic sequence.
From part 1 it is clear that the nth term of the given arithmetic sequence is:
[tex]a_n=5n-4[/tex]
Putting [tex]n=10[/tex], we get
[tex]a_{10}=5(10)-4[/tex]
[tex]a_{10}=50-4[/tex]
[tex]a_{10}=46[/tex]
Therefore, the 10th term of the given arithmetic sequence is 46.
