Answer:
1. Geometric sequence
2. 4,096
3. 5,460
Step-by-step explanation:
Part 1
Since the number of letters sent is multiplied by 4 for any subsequent term, the sequence is an example of a geometric sequence as it grows exponentially.
Part 2
Given a geometric sequence, the nth term is determined using the formula:
[tex]T_n=ar^{n-1},$ where r=common ratio, a=first term, n=number of terms[/tex]
In this case,
a=1 (i.e. Nyah)
r=4
Since we want to determine how many letters will be sent on the sixth mailing(i.e after Nyah), n=7
Substituting
[tex]T_6=1*4^{7-1}\\=4^6\\=4096[/tex]
Part 3
To determine how many people would have participated by the sixth mailing, we are required to find the sum of the first seven terms of the geometric sequence.
We use the sum of a geometric sequence formula
[tex]S_n=\dfrac{a(r^n-1)}{r-1} \\S_7=\dfrac{1(4^7-1)}{4-1} \\=\dfrac{16383}{3}\\\\=5461[/tex]
Therefore, excluding Nyah, 5460 people would have participated by the sixth mailing.
Answer:
1. Geometric sequence
2. 4,096
3. 5,460
Step-by-step explanation:
