Question

The tallest of a collection of wooden dolls stands 1 meter tall, and each successive doll is
half as tall as the one before it. If there are 8 dolls in the collection, which is closest to
the combined height of the dolls?
O A. 1.5 meters
O B. 2 meters
O C. 3.1 meters
O D.
4 meters

Answer 1

The combined height of the dolls when the tallest of a collection of wooden dolls stands 1 meter tall, and each successive doll is half as tall as the one before it is 2 meters.

What is geometric sequence?

Geometric sequence is the sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.

It can be given as,

$S=\dfrac{a(1-r^n)}{1-r}$

Here, $a_1$ is the first term of the sequence, n is the number of terms, and r is the common ratio.

The tallest of a collection of wooden dolls stands 1 meter tall, and each successive doll is half as tall as the one before it.

The second doll is half of the first doll. Thus, the height of the second doll is,

$a_2=\dfrac{1}{2}\\a_2=0.5\rm\;m$

Similarly, height of third doll,

$a_3=\dfrac{0.5}{2}\\a_3=0.25\rm\;m$

Here, we see a pattern or sequence in the height of doll,

1,0.5,0.25......

For this series, the value of first term $a_1$ is 1, the number of dolls n is 8 and common ratio r is 0.5. Put the value in the above formula,

$S=\dfrac{1(1-0.5^8)}{1-0.5}\\S=1.992\\S\approx 2\rm\; meters$

Thus, the combined height of the dolls when the tallest of a collection of wooden dolls stands 1 meter tall, and each successive doll is half as tall as the one before it is 2 meters.

Learn more about the geometric sequence here;

https://brainly.com/question/1509142

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