Question

Please can someone help there 10 Points for it!!!!

Answer 1

a) The missing terms are 9, 13, 21 and 25.

b) If we know that
`n_(1) = 9` and
`r = 4`, then the n-th term of the sequence is represented by
`n_(n) = 9 +4\cdot (n-1)`.

Explanation:

a) Given that elements of the sequence are found by increasing by the same amount, we infer that elements are part of an arithmetical progression. The rate of progression is now determined:

`3\cdot r = 29-17`

`3\cdot r = 12`

`r = 4`

The missing terms are:

`n_(1) = 17 - 2\cdot (4)`

`n_(1) = 9`

`n_(2) = 17 - 4`

`n_(2) = 13`

`n_(4) = 17 +4`

`n_(4) = 21`

`n_(5) = 17 + 2\cdot (4)`

`n_(5) = 25`

The missing terms are 9, 13, 21 and 25.

b) The formula for the arithmetical progression is represented by the following formula:

`n_(n) = n_(1) + r\cdot (n-1)` (1)

Where:

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

`n` - Indicator associated with the element of the sequence.

`r` - Progression rate.

If we know that
`n_(1) = 9` and
`r = 4`, then the n-th term of the sequence is represented by
`n_(n) = 9 +4\cdot (n-1)`.