Chain Mail problem?

In the first stage of a chain e-mail, four people send a message to four of their friend. In the second stage, each person who recieved the message forwards it to four of their friends. The number of stages required for one million people to have recieved the e-mail is..........?

how do you do this problem?

Here's another problem:
if 3a, 2a-1, and 7a +8 form a geometric sequence, the value of the first term is....?

Stage 1) 4 people RECIEVE
Stage 2) 16 people RECIEVE
Stage 3) 64 people RECIEVE
......
Geomtric row with term 1 = 4 and reason = 4
sum of the first n terms = (q^n-1)/(q-1) = (4^n-1)/3
4^n-1=3million
4^n=2999999
n=log(2999999)/log(4)
n~10,7..
n=11

Other prob :
(2a-1)/(3a) = q
(7a+8)/(2a-1)=q
(2a-1)/(3a)=(7a+8)/(2a-1)
(2a-1)*(2a-1)=(7a+8)(3a)
4a虏-4a+1=21a虏+24a
17a虏+28a-1=0
D=716

a1 = (-28+sqrt716)/34
a2 = (-28-sqrt716)/34

It's a pattern:

Image this: Four people send out the message to four others each. This means we have 4+4+4+4, or 4^2. We now have 16 emails. From here, each of these four send it out to four others. Take it one '4' at a time.

The first four will send it to 16, as we determined from the second stage. This would make it 16*4, as there are 4 people in the second stage each sending it out to 16 people each. This makes 64 emails now.

Take this number and do the same. Each of these people are sending it out to four others each, so that's another 16 emails each. This makes an equation y = 4x, where x is the number of people. Notice how the stages go in powers of 4, where stage one has the number of people equal to 4^1, stage two has the number of people equal to 4^2, stage 3 has the number of people equal to 4^3, etc.

Now use this equation and plug in 1,000,000.

1000000 = 4x
250000 = x

So now, we know the number of people needed. But what stage is this? Use a log for this.

4^x = 250,000
Be = N
logb(N) = e

B = 4
e = x
N = 250,000

So, rewrite it:

log4(250,000) = x
Use the change of base formula, which is (logN/logb) to determine x.

log250000/log4 = 8.965784285

This means you need about 8.9 stages to reach 1m people, but since you can't have part of a stage, you'll need to round UP to be greater than or equal to 1m.

You need 9 stages.