Question

Find an explicit formula for the geometric sequence -40,-20,-10......

Note: the first term should be c(1).

c(n)= ?

​

Answer 1

The explicit formula for the geometric sequence is
`c(n) = -40\cdot \left((1)/(2) \right)^(n-1)`.

Explanation:

By definition of geometric sequence, we should use the following expression:

`c(n) = c_(1)\cdot r^(n-1)`,
`n \ge 1` (1)

Where:

`c_(1)` - First term.

`r` - Geometric rate.

`n` - Position of the element within the series.

If we know that
`c_(1) = -40` and
`r = (1)/(2)`, then the explicit formula for the geometric sequence is:

`c(n) = -40\cdot \left((1)/(2) \right)^(n-1)`

The explicit formula for the geometric sequence is
`c(n) = -40\cdot \left((1)/(2) \right)^(n-1)`.