Question

1. (2 points) The starship Enterprise just picked up a strange creature called a tribble.

At first there was only one, but overnight the tribble spawned 3 more tribbles just like
it. The next night, each tribble spawned 3 more tribbles, and this continued happening
each night. How many tribbles were on the starship after the 7th night? (Hint: Show
that the number of tribbles follows the geometric series.)


Pls help y’all

Answer 1

21 tribbles on the 7th night

Explanation:

every night 3 tribbles appear meaning that the tribbles spawn rate is y=3x

y= number of tribbles

x= number of nights

Answer 2

The number of tribbles that were on the starship after the 7th night is equal to 729 tribbles.

In Mathematics and Geometry, the nth term of any geometric sequence can be determined by using the following formula:

`a_n=a_1(r)^(n-1)`

Where:

• 
  `a_n` is the nth term of any geometric sequence.
• r represents the common ratio.
• 
  `a_1` represents the first term of any geometric sequence.

Based on the information provided about the number of tribbles, we have the following geometric series;

1, 3, 9, ......

For the common ratio, we have;

Common ratio, r = 3/1 = 9/3

Common ratio, r = 3.

Now, we can write an explicit equation for the nth term of this geometric sequence;

`a_n=a_1(r)^(n-1)\\\\a_n=1(3)^(n-1)\\\\a_7=(3)^(7-1)\\\\a_7=3^6\\\\a_7=729\;tribbles`