Answer:
a) The missing terms are 9, 13, 21 and 25.
b) If we know that
and
, then the n-th term of the sequence is represented by
.
Step-by-step explanation:
a) Given that elements of the sequence are found by increasing by the same amount, we infer that elements are part of an arithmetical progression. The rate of progression is now determined:
![3\cdot r = 29-17](https://tex.z-dn.net/?f=3%5Ccdot%20r%20%3D%2029-17)
![3\cdot r = 12](https://tex.z-dn.net/?f=3%5Ccdot%20r%20%3D%2012)
![r = 4](https://tex.z-dn.net/?f=r%20%3D%204)
The missing terms are:
![n_{1} = 17 - 2\cdot (4)](https://tex.z-dn.net/?f=n_%7B1%7D%20%3D%2017%20-%202%5Ccdot%20%284%29)
![n_{1} = 9](https://tex.z-dn.net/?f=n_%7B1%7D%20%3D%209)
![n_{2} = 17 - 4](https://tex.z-dn.net/?f=n_%7B2%7D%20%3D%2017%20-%204)
![n_{2} = 13](https://tex.z-dn.net/?f=n_%7B2%7D%20%3D%2013)
![n_{4} = 17 +4](https://tex.z-dn.net/?f=n_%7B4%7D%20%3D%2017%20%2B4)
![n_{4} = 21](https://tex.z-dn.net/?f=n_%7B4%7D%20%3D%2021)
![n_{5} = 17 + 2\cdot (4)](https://tex.z-dn.net/?f=n_%7B5%7D%20%3D%2017%20%2B%202%5Ccdot%20%284%29)
![n_{5} = 25](https://tex.z-dn.net/?f=n_%7B5%7D%20%3D%2025)
The missing terms are 9, 13, 21 and 25.
b) The formula for the arithmetical progression is represented by the following formula:
(1)
Where:
- First element of the sequence.
- Indicator associated with the element of the sequence.
- Progression rate.
If we know that
and
, then the n-th term of the sequence is represented by
.
Answer
254 feet
explanation
212 + (14 x 3)
Step-by-step explanation:
Let's take the RHS,
we've,
<h3>(<u>Cosa</u><u>/</u><u>2</u><u> </u><u>-</u><u> </u><u>sina</u><u>/</u><u>2</u><u>)</u></h3><h3>(<u>Cosa/</u><u>2</u><u> </u><u>+</u><u> </u><u>sina</u><u>/</u><u>2</u><u>)</u></h3>
Let's Rationalise the Denominator.
we get,
<h3>(<u>Cosa/</u><u>2</u><u> </u><u>-</u><u> </u><u>sina</u><u>/</u><u>2</u><u>)</u><u>^</u><u>2</u></h3><h3><u>(</u><u>cosa</u><u>/</u><u>2</u><u>)</u><u>^</u><u>2</u><u> </u><u>-</u><u> </u><u>(</u><u>sina</u><u>/</u><u>2</u><u>)</u><u>^</u><u>2</u></h3>
The numerator is in form of (a-b)^2 and the denominator is in form of a^2-b^2. Now,
By formula,
<h3>(<u>Cosa/</u><u>2</u><u>)</u><u>^</u><u>2</u><u> </u><u>-2cosa</u><u>/</u><u>2</u><u>.</u><u>s</u><u>i</u><u>n</u><u>a</u><u>/</u><u>2</u><u> </u><u>+</u><u> </u><u>(</u><u>sina</u><u>/</u><u>2</u><u>)</u><u>^</u><u>2</u> </h3><h3> cosa</h3>
Here I substituted Cosa in place of (Cosa/2)^2 - (sina/2)^2 because it's the formula of cosa in sub multiple angle form.
<h3>In the numerator, </h3>
(sina/2)^2 + (Cosa/2)^2 =1.........( by formula)
so we have,
<h3><u>1</u><u> </u><u>-</u><u> </u><u>2</u><u>s</u><u>i</u><u>n</u><u>a</u><u>/</u><u>2</u><u>.</u><u>c</u><u>o</u><u>s</u><u>a</u><u>/</u><u>2</u></h3><h3>Cosa</h3>
<h3 /><h3 /><h3><u>1</u><u> </u><u>-</u><u> </u><u>sina</u> {because 2sina/2.cosa/2=sina)</h3><h3>Cosa</h3>
LHS proved.
Thank You.
Answer:
99 degrees
Step-by-step explanation:
angle 8 = 99 degrees because corresponding or 'f shaped' angles are equal
Answer:
Step-by-step explanation:
The first term is 6. The difference between the first two terms is 6. The first differences are 6,8,10,12,etc. so the second differences are 2’s.
quadratic formula: an^2+bn+c
2a=second difference=2
3a+b=first differece =6
a+b+c=first term=6
substitute: a=2/2=1, 3(1)+b=6 so b=3, 1+3+c=6 so c=2
nth term= n^2+3n +2