Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Get immediate and reliable answers to your questions from a community of experienced professionals on our platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
Given:
[tex]\phi=1.618[/tex]
22nd number in Fibonacci sequence = 17,711
To find:
The 23rd number in the Fibonacci sequence.
Solution:
The nth term of a Fibonacci sequence is:
[tex]f_n=\dfrac{\phi^n-(1-\phi)^n}{\sqrt{5}}[/tex]
Substituting [tex]\phi=1.618, n=21[/tex], we get
[tex]f_{21}=\dfrac{(1.618)^{21}-(1-1.618)^{21}}{\sqrt{5}}[/tex]
[tex]f_{21}=\dfrac{(1.618)^{21}-(1-1.618)^{21}}{\sqrt{5}}[/tex]
[tex]f_{21}=10941.1724024[/tex]
[tex]f_{21}\approx 10941[/tex]
Now,
[tex]f_{23}=f_{21}+f_{22}[/tex]
[tex]f_{23}=10941+17711[/tex]
[tex]f_{23}=28652[/tex]
It is about 28,656. Therefore, the correct option is D.
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.
