Question

Nyah receives a chain letter and has to copy the letter and send it to 4 of her friends,

have to copy the letter and send it to 4 other friends, and so on.


Finding the number of letters sent on the nth mailing is an example of


a geometric sequence


COMPLETE


If everyone who receives a letter participates, how many letters will be sent on the si


54 X = 4,096


COMPLETE


By the sixth mailing, how many people will have participated since the start?


DONE


I need the last part

Answer 1

1. Geometric sequence

2. 4,096

3. 5,460

Explanation:

Answer 2

1. Geometric sequence

2. 4,096

3. 5,460

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:

`T_n=ar^(n-1),$ where r=common ratio, a=first term, n=number of terms`

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

`T_6=1*4^(7-1)\\=4^6\\=4096`

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

`S_n=(a(r^n-1))/(r-1) \\S_7=(1(4^7-1))/(4-1) \\=(16383)/(3)\\\\=5461`

Therefore, excluding Nyah, 5460 people would have participated by the sixth mailing.