Question

Use the given sequence to answer this following questions:

Answer 1

Given:

The arithmetic sequence is:

$1, 6, 11, 16, 21,...$

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,

$1, 6, 11, 16, 21,...$

Here, the first term is 1 and the common difference is:

$d=a_2-a_1$

$d=6-1$

$d=5$

The nth term of an arithmetic sequence is:

$a_n=a+(n-1)d$

Where, a is the first term and d is the common difference.

Putting $a=1,\ d=5$, we get

$a_n=1+(n-1)5$

$a_n=1+5n-5$

$a_n=5n-4$

Therefore, the nth term of the given sequence is $a_n=5n-4$.

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:

$a_n=5n-4$

Putting $n=10$, we get

$a_{10}=5(10)-4$

$a_{10}=50-4$

$a_{10}=46$

Therefore, the 10th term of the given arithmetic sequence is 46.