Question

Which geometric series results in a sum of -69,905

Answer 1

Using geometric sequence concepts, it is found that the one which results in a sum of -69,905 is:

D. $\sum_{k = 0}^{9} -\frac{1}{5}(4)^k$

What is a geometric sequence?

• A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

As a sum, it can be represented by:

$\sum_{k = 0}^{n - 1} a_1(q)^k$

• In which $a_1$ is the first term.

The result of the sum is:

$S = \frac{a_1(1 - q^n)}{1 - q}$

Item A:

For this sequence, we have that:

$a_1 = \frac{1}{4} = 0.25, n = 8, q = -5$

Hence, the sum is:

$S = \frac{0.25(1 - (-5)^8)}{4} = -24414$

Item B:

For this sequence, we have that:

$a_1 = -\frac{1}{4} = -0.25, n = 12, q = 5$

Hence, the sum is:

$S = \frac{-0.25(1 - (5)^12)}{-4} = -15258789$

Item C:

For this sequence, we have that:

$a_1 = \frac{1}{5} = 0.2, n = 11, q = -4$

Hence, the sum is:

$S = \frac{0.2(1 - (-4)^11)}{3} = 279620.3$

Item D:

For this sequence, we have that:

$a_1 = -\frac{1}{5} = -0.2, n = 10, q = 4$

Hence, the sum is:

$S = \frac{-0.2(1 - (4)^10)}{-3} = -69905$

Hence option D is correct.

You can learn more about geometric sequence concepts at https://brainly.com/question/11847927