Answer:
The person has62 ancestors going back five generations.
The person has 2046 ancestors going back ten generations.
---------------------
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:
Where a is the first term and r is the commom factor.
The sum of the first n elements of a geometric sequence is:
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:
The person has 62 ancestors going back five generations.
2) Going back 10 generations:
S when n = 10, so:
The person has 2046 ancestors going back ten generations.
-------------
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:
.
We have the following sequence
, in which is the child's height at age 8.
We have that:
So
.
The child's height at age 8 would be 127.2 cm.