An arithmetic sequence is a string of numbers that is produced by repeatedly applying a certain arithmetic operation, in this case the string of numbers 
is thus determined, the first term 
is equivalent to number 23 and each next term, 
with 
(i.e. 
) is calculated using the given formula 
, so the next term in the sequence, 
will be:
in the same way the following terms are calculated
Another way to achieve this is to use the formula to calculate the terms , note that:
So, as you see each tn becomes minus a multiple of -3, or what is the same:
Replacing the desired value
Answer
the value of n when 
is 
, 
Answer:
We know that:
Tan(x) = sin(x)/cos(x)
We know that:
Tan(θ) = 1 = sin(θ)/cos(θ)
we can rewrite this as:
sin(θ)/cos(θ) = 1
sin(θ) = cos(θ)
If you know the table of notable angles, the angle such that this is true is θ = 45°
sin(45°) = 1/√2 = cos(45°)
Now we want to find the value of:
sec(θ) + cosec(θ)
Where:
sec(θ) = 1/cos(θ)
cosec(θ) = 1/sin(θ)
And we already know the values of the sine and cosine function, then:
sec(45°) + cosec(45°) = 1/cos(45°) + 1/sin(45°) = 2*(1/( 1/√2)) = 2*√2
Then, given that:
Tan(θ) = 1
We can conclude that:
sec(θ) + cosec(θ) = 2*√2
Answer:
Explanation:
Here, we want to get the sequence type
In an arithmetic sequence, the difference between terms is the same
For a geometric sequence, the division of a succeeding term by a preceding term would yield the term called the common ratio
Now, let us consider the differences:
This means that the sequence is not arithmetic
Now, let us test if geometric
Mathematically, we have that as:
This means that the given sequence is geometric
Answer:
6
Step-by-step explanation:
As you might know, the two lines surrounding the -4 represent the absolute value, which is basically the distance from 0, and the distance is always positive. To clear any confusion, the absolute value of positive number will not be it's opposite because remember, distance is always positive, so absolute value is always positive (because it is basically the distance from zero).
To help, here is an example (that is not related to the problem!):
|-6| = 6
|6| = 6
<em>Now, back to the problem...</em>
Since you now know that the absolute value is always positive, |-4| would equal 4. So now you have:
4 - 8 + 10 = ???
From here, you can just solve and the answer is 6, so:
4 - 8 + 10 = 6
You final answer is 6.
Hope this helped somehow :D
You have the correct sequence of reasons
Here's what the full step by step picture looks like
3.25(1.25x + 0.5) = 10.5 ................ given
4.0625x + 1.625 = 10.5 ................ distributive property
4.0625x = 8.875 ................ subtraction property of equality
x = 2.18461538461539 ....... division property of equality
---------------------------
Notes:
- The decimal value of x is approximate. Round it however you need.
- In the third step, we subtracted 1.625 from both sides
- In the fourth step, we divide both sides by 4.0625
