Question

Please show me step by step how to do this

Answer 1

The next three terms of the sequence are 17, 21 and 25.

The 300th term of the sequence is 1197.

Explanation:

The statement describes an arithmetic progression, which is defined by following formula:

`p(n) = p_(1)+r\cdot (n-1)` (1)

Where:

`p_(1)` - First element of the sequence.

`r` - Progression rate.

`n` - Index of the n-th element of the sequence.

`p(n)` - n-th element of the series.

If we know that
`p_(1) = 1`,
`n = 2` and
`p(n) = 5`, then the progression rate is:

`r = (p(n)-p_(1))/(n-1)`

`r = 4`

The set of elements of the series are described by
`p(n) = 1 + 4\cdot (n-1)`.

Lastly, if we know that
`n = 300`, then the 300th term of the sequence is:

`p(n) = 1 + 4\cdot (n-1)`

`p(n) = 1197`

And the next three terms of the sequence are:

n = 5

`p(n) = 1 + 4\cdot (n-1)`

`p(n) = 17`

n = 6

`p(n) = 1 + 4\cdot (n-1)`

`p(n) = 21`

n = 7

`p(n) = 1 + 4\cdot (n-1)`

`p(n) = 25`

The next three terms of the sequence are 17, 21 and 25.

The 300th term of the sequence is 1197.