Connect - Learn - Fundraise
First time here? Checkout the FAQs!
x

*Math Image Search only works best with zoomed in and well cropped math screenshots. Check DEMO



Our AI technology rapidly solves problems, while our available tutors provide personalized support and clarification to ensure efficient and effective solutions.


2 like 0 dislike
291 views
3;3;6;9;15;... are the first five terms of a quadratic pattern. Write down the value of the sixth term (T6) of the pattern.
in Mathematics by | 291 views

2 Answers

0 like 0 dislike
Best answer

The sixth term is 24 as shown below.

\(\begin{aligned} 3,3,6,9,15 & \\ 3+3 &=6 \\ 3+6 &=9 \\ 6+9 &=15 \\ 9+15 &=24 \\ \therefore 3 ; 3 ; 6 ; 9 ; 15 ; 24 \end{aligned}\)

sequence

by Diamond (45,822 points)
1 like 0 dislike
\[
a_{n}=3 F_{n}=\frac{3\left(\phi^{n}-(-\phi)^{-n}\right)}{\sqrt{5}}
\]
Explanation:
This is 3 times the standard Fibonacci sequence.
Each term is the sum of the two previous terms, but starting with 3,3 , instead of 1,1 .
The standard Fibonnaci sequence starts:
\[
1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987, \ldots
\]
The terms of the Fibonacci sequence can be defined iteratively as:
\[
\begin{aligned}
&F_{1}=1 \\
&F_{2}=1 \\
&F_{n+2}=F_{n}+F_{n+1}
\end{aligned}
\]
The general term can also be expressed by a formula:
\[
F_{n}=\frac{\phi^{n}-(-\phi)^{-n}}{\sqrt{5}}
\]

where \(\phi=\frac{1}{2}+\frac{\sqrt{5}}{2} \approx 1.618033988\)
So the formula for a term of our example sequence can be written:
\[
a_{n}=3 F_{n}=\frac{3\left(\phi^{n}-(-\phi)^{-n}\right)}{\sqrt{5}}
\]
by Diamond (89,326 points)

Related questions

1 like 0 dislike
1 answer
0 like 0 dislike
1 answer
1 like 1 dislike
1 answer
0 like 1 dislike
0 answers

Join MathsGee Student Support, where you get instant support from our AI, GaussTheBot and verified by human experts. We use a combination of generative AI and human experts to provide you the best solutions to your problems. Ask a question now!


On the MathsGee Student Support, you can:


1. Get instant answer to your questions


2. Get expert-verified answers


3. Vote on questions and answers


4. Tip your favorite community members


5. Join expert live video sessions (Paid/Free)


6. Earn points by participating


7. Start a Fundraiser


8. Take a course


9. Enjoy our interactive learning resources



Posting on the MathsGee Student Support


1. Remember the human


2. Act like you would in real life


3. Find original source of content


4. Check for duplicates before publishing


5. Read the community guidelines




MathsGee Student Support Rules


1. Answers to questions will be posted immediately after moderation


2. Questions will be queued for posting immediately after moderation


3. Depending on the number of messages we receive, you could wait up to 24 hours for your message to appear. But be patient as posts will appear after passing our moderation.




MathsGee Student Support

MathsGee Student Support