Question

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.

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.