Question

Consider the following geometric sequence. -5,10,-20,40... If the explicit formula for the sequence above is expressed...

Answer 1

Answer:

The explicit formula for the geometric sequence is given by:

$a_n = a_1 \cdot r^{n-1}$

where,

$a_1$ si the first term

r is the common ratio of the terms.

As per the statement:

Consider the following geometric sequence. -5, 10, -20, 40...

First term($a_1$) = -5

Common ratio(r) = -2

Since,

$\frac{10}{-5} = -2$,

$\frac{-20}{10} = -2$,

$\frac{40}{-20} = -2$ and so on...

Substitute the given values in [1] we have;

$a_n = -5 \cdot (-2)^{n-1}$ where, n is the number of term.

On comparing the equation  $a_n = -5 \cdot (-2)^{n-1}$  with $a_n = b \cdot c^{n-1}$ we get;

b = -5 and c = -2

Therefore, the values of b and c are:

b = -5 and c = -2

Answer 2

To fit the formula, b is the first term, -5, and c is the common ratio, or -2