Answer:
Proved (See Explanation)
Step-by-step explanation:
Show that 3ⁿ⁺⁴ - 3ⁿ is divisible by 16.
This is done as follows
From laws of indices;
aᵐ⁺ⁿ = aᵐ * aⁿ.
So, 3ⁿ⁺⁴ can be written as 3ⁿ * 3⁴.
becomes
Factorize
3ⁿ * 5
5(3ⁿ)
<em>The expression can not be further simplified.</em>
<em>However, we can conclude that when 3ⁿ⁺⁴ - 3ⁿ is divisible by 16, because 5(3ⁿ) is a natural whole number as long as n is a natural whole number.</em>
Given:
The multiples of 2 form a sequence as follows: 2, 4, 6, 8, 10, 12, 14, 16, ...
To find:
Description of the sequence you see. What about the multiples of three? Four? Five?
Solution:
The multiples of 2 form a sequence as follows:
2, 4, 6, 8, 10, 12, 14, 16, ...
It is defined as , where n is a natural number. It represents all positive even numbers.
Multiples of 3, 4 and 5 form the respective sequences:
, i.e., 3, 6, 9, 12, 15, 18, 21, 24,...
, i.e., 4, 8, 12, 16, 20, 24, 28, 32...
, i.e., 5, 10, 15, 20, 25, 30, 35, 40...