Question

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

Answer 1

Answer:

The explicit formula for the geometric sequence is $c(n) = -40\cdot \left(\frac{1}{2} \right)^{n-1}$.

Step-by-step 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 $r = \frac{1}{2}$, then the explicit formula for the geometric sequence is:

$c(n) = -40\cdot \left(\frac{1}{2} \right)^{n-1}$

The explicit formula for the geometric sequence is $c(n) = -40\cdot \left(\frac{1}{2} \right)^{n-1}$.