Respuesta :
Answer:
The person has62 ancestors going back five generations.
The person has 2046 ancestors going back ten generations.
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The child's height at age 8 would be 127.2 cm.
Step-by-step explanation:
The first sequence is a geometric sequence.
In a geometric sequence, each term is found by multiplying the previous term by a constant r.
We write a geometric sequence like this:
[tex]{a, ar, ar^{2}, ar^{3},...}[/tex]
Where a is the first term and r is the commom factor.
The sum of the first n elements of a geometric sequence is:
[tex]S = \frac{a(1 - r^{n})}{1-r}[/tex]
So, for the first exercise, our geometric sequence is:
{2,4,8,...},
so a = 2 and r = 2.
1)Find the total number of ancestors a person has going back five generations
S when n = 5, so:
[tex]S = \frac{a(1 - r^{n})}{1-r} = \frac{2*(1-2^{5})}{1-2} = 62[/tex]
The person has 62 ancestors going back five generations.
2) Going back 10 generations:
S when n = 10, so:
[tex]S = \frac{a(1 - r^{n})}{1-r} = \frac{2*(1-2^{10})}{1-2} = 2046[/tex]
The person has 2046 ancestors going back ten generations.
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The following question is related to an arithmetic sequence:
An arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant.
If the first term of an arithmetic sequence is a1 and the common difference is d, then the nth term of the sequence is given by:
[tex]a_{n} = a_{1} + (n-1)d[/tex].
We have the following sequence
[tex]98.2, a_{2}, 109.8, a_{4}, a_{5}, a_{6}[/tex], in which [tex]a_{6}[/tex] is the child's height at age 8.
We have that:
[tex]d = \frac{109.8 - 98.2}{2} = 5.8[/tex]
So
[tex]a_{6} = a_{1} + 5d = 98.2 + 5*5.8 = 127.2[/tex].
The child's height at age 8 would be 127.2 cm.
