Question

Consider the sequence -101, -91, -81, -71, ...

Determine an explicit formula for the nth term of the sequence

Answer 1

Answer:
`t_(n)` = 10n - 111

Explanation:

The first term of the sequence is - 101

we need to confirm that the sequence is arithmetic , that is , if it is arithmetic , it must have a common difference (d).

d = second term - first term = third term - second term

d = -91 - (-101)

d = -91 + 101

d = 10

Therefore the formula for the nth term is given as:

`t_(n)`= a + (n - 1 ) d

`t_(n)` = - 101 + (n - 1) 10

`t_(n)` = - 101 + 10n - 10

`t_(n)` = -111 + 10n

Therefore :

`t_(n)` = 10n - 111