Use the given sequence to answer this following questions: 1, 6, 11, 16, 21, ...
1. Write a rule for the nth term of the arithmetic sequence. (Do not put any spaces between terms when writing the rule.)
2 find the tenth term.

Given:

The arithmetic sequence is:

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,

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

The nth term of an arithmetic sequence is:

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

Putting , we get

Therefore, the nth term of the given sequence is .

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:

Putting , we get

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

a negative exponent is translated as follows:

so, we have