Deriving a Formula in Solving Reverse Fibonacci Means
Reverse Fibonacci sequence $\{J_n\}$ is defined by the relation $J_n = 8(J_{n-1} - J_{n-2})$ for $n\geq2$ with $J_0=0$ and $J_1=1$ as initial terms. A few formulas have been derived for solving the missing terms of a sequence in books and mathematical journals, but not for the reverse Fibonacci sequ...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Center for Policy, Research and Development Studies
2022-12-01
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| Series: | Recoletos Multidisciplinary Research Journal |
| Subjects: | |
| Online Access: | https://rmrj.usjr.edu.ph/rmrj/index.php/RMRJ/article/view/1200 |
| _version_ | 1797962588261187584 |
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| author | Steven Elizalde Romeo Patan |
| author_facet | Steven Elizalde Romeo Patan |
| author_sort | Steven Elizalde |
| collection | DOAJ |
| description | Reverse Fibonacci sequence $\{J_n\}$ is defined by the relation $J_n = 8(J_{n-1} - J_{n-2})$ for $n\geq2$ with $J_0=0$ and $J_1=1$ as initial terms. A few formulas have been derived for solving the missing terms of a sequence in books and mathematical journals, but not for the reverse Fibonacci sequence. Thus, this paper derived a formula that deductively solves the first missing term $\{x_1\}$ of the reverse Fibonacci sequence and is given by the equation
$x_1=\frac{b+8aJ_n}{J_{n+1}}$.
By using the derived formula for $\{x_1\}$, it is now possible to solve the means of the reverse Fibonacci sequence as well as solving the sequence itself. |
| first_indexed | 2024-04-11T01:15:33Z |
| format | Article |
| id | doaj.art-bf2b2f0c1ae1452fa40b44203ec03940 |
| institution | Directory Open Access Journal |
| issn | 2423-1398 2408-3755 |
| language | English |
| last_indexed | 2024-04-11T01:15:33Z |
| publishDate | 2022-12-01 |
| publisher | Center for Policy, Research and Development Studies |
| record_format | Article |
| series | Recoletos Multidisciplinary Research Journal |
| spelling | doaj.art-bf2b2f0c1ae1452fa40b44203ec039402023-01-04T05:20:38ZengCenter for Policy, Research and Development StudiesRecoletos Multidisciplinary Research Journal2423-13982408-37552022-12-01102414510.32871/rmrj2210.02.03Deriving a Formula in Solving Reverse Fibonacci MeansSteven Elizalde0https://orcid.org/0000-0003-2075-7521Romeo Patan1https://orcid.org/0000-0003-1467-333XNorth Eastern Mindanao State University, Surigao del Sur, PhilippinesNorth Eastern Mindanao State University, Surigao del Sur, PhilippinesReverse Fibonacci sequence $\{J_n\}$ is defined by the relation $J_n = 8(J_{n-1} - J_{n-2})$ for $n\geq2$ with $J_0=0$ and $J_1=1$ as initial terms. A few formulas have been derived for solving the missing terms of a sequence in books and mathematical journals, but not for the reverse Fibonacci sequence. Thus, this paper derived a formula that deductively solves the first missing term $\{x_1\}$ of the reverse Fibonacci sequence and is given by the equation $x_1=\frac{b+8aJ_n}{J_{n+1}}$. By using the derived formula for $\{x_1\}$, it is now possible to solve the means of the reverse Fibonacci sequence as well as solving the sequence itself.https://rmrj.usjr.edu.ph/rmrj/index.php/RMRJ/article/view/1200fibonacci sequencereverse fibonacci sequencebinet’s formulameans |
| spellingShingle | Steven Elizalde Romeo Patan Deriving a Formula in Solving Reverse Fibonacci Means Recoletos Multidisciplinary Research Journal fibonacci sequence reverse fibonacci sequence binet’s formula means |
| title | Deriving a Formula in Solving Reverse Fibonacci Means |
| title_full | Deriving a Formula in Solving Reverse Fibonacci Means |
| title_fullStr | Deriving a Formula in Solving Reverse Fibonacci Means |
| title_full_unstemmed | Deriving a Formula in Solving Reverse Fibonacci Means |
| title_short | Deriving a Formula in Solving Reverse Fibonacci Means |
| title_sort | deriving a formula in solving reverse fibonacci means |
| topic | fibonacci sequence reverse fibonacci sequence binet’s formula means |
| url | https://rmrj.usjr.edu.ph/rmrj/index.php/RMRJ/article/view/1200 |
| work_keys_str_mv | AT stevenelizalde derivingaformulainsolvingreversefibonaccimeans AT romeopatan derivingaformulainsolvingreversefibonaccimeans |