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A series in which any term is the sum of the preceding two terms is called a Fibonacci series. The first two terms are given initially and together they determine the entire series. If the difference of the squares of the ninth and the eighth terms of a Fibonacci series is 715 then, what is the 12th term of that series?
- a)157
- b)142
- c)144
- d)Cannot be determined
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A series in which any term is the sum of the preceding two terms is ca...
The series is like 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144...
The difference is 715 and the 12th term is 144.
The difference is 715 and the 12th term is 144.
Most Upvoted Answer
A series in which any term is the sum of the preceding two terms is ca...
Given:
- The difference of the squares of the ninth and the eighth terms of a Fibonacci series is 715.
To find:
- The 12th term of that series.
Approach:
- We can use the formula to find the nth term of a Fibonacci series: Fn = Fn-1 + Fn-2
- We can also use the given information to form equations and solve for the required term.
Solution:
Let's assume that the first two terms of the Fibonacci series are a and b, then we can write the series as:
a, b, a+b, 2b+a, 3b+2a, 5b+3a, 8b+5a, 13b+8a, 21b+13a, ...
We are given that the difference of the squares of the ninth and the eighth terms of the series is 715, so we can write the equation as follows:
(21b+13a)^2 - (13b+8a)^2 = 715
Simplifying the equation, we get:
(8a+21b+13a+13b)(8a+21b-13a-13b) = 715
(21a+34b)(-5a+8b) = 715
We can find two factors of 715 whose difference is 13*2*5 = 130, which are 65 and 11:
(21a+34b) = 65 and (-5a+8b) = 11
Solving these equations, we get: a = 2 and b = 1.
Now, we can use the formula to find the 12th term of the series:
F12 = F11 + F10
F10 = F9 + F8
F11 = F10 + F9
Using these equations, we can find that F9 = 34, F8 = 21, F10 = 55, and F11 = 89.
Therefore, F12 = F11 + F10 = 89 + 55 = 144.
Hence, the correct answer is option (c) 144.
- The difference of the squares of the ninth and the eighth terms of a Fibonacci series is 715.
To find:
- The 12th term of that series.
Approach:
- We can use the formula to find the nth term of a Fibonacci series: Fn = Fn-1 + Fn-2
- We can also use the given information to form equations and solve for the required term.
Solution:
Let's assume that the first two terms of the Fibonacci series are a and b, then we can write the series as:
a, b, a+b, 2b+a, 3b+2a, 5b+3a, 8b+5a, 13b+8a, 21b+13a, ...
We are given that the difference of the squares of the ninth and the eighth terms of the series is 715, so we can write the equation as follows:
(21b+13a)^2 - (13b+8a)^2 = 715
Simplifying the equation, we get:
(8a+21b+13a+13b)(8a+21b-13a-13b) = 715
(21a+34b)(-5a+8b) = 715
We can find two factors of 715 whose difference is 13*2*5 = 130, which are 65 and 11:
(21a+34b) = 65 and (-5a+8b) = 11
Solving these equations, we get: a = 2 and b = 1.
Now, we can use the formula to find the 12th term of the series:
F12 = F11 + F10
F10 = F9 + F8
F11 = F10 + F9
Using these equations, we can find that F9 = 34, F8 = 21, F10 = 55, and F11 = 89.
Therefore, F12 = F11 + F10 = 89 + 55 = 144.
Hence, the correct answer is option (c) 144.
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A series in which any term is the sum of the preceding two terms is called a Fibonacci series. The first two terms are given initially and together they determine the entire series. If the difference of the squares of the ninth and the eighth terms of a Fibonacci series is 715 then, what is the 12th term of that series?a)157b)142c)144d)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer?
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A series in which any term is the sum of the preceding two terms is called a Fibonacci series. The first two terms are given initially and together they determine the entire series. If the difference of the squares of the ninth and the eighth terms of a Fibonacci series is 715 then, what is the 12th term of that series?a)157b)142c)144d)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A series in which any term is the sum of the preceding two terms is called a Fibonacci series. The first two terms are given initially and together they determine the entire series. If the difference of the squares of the ninth and the eighth terms of a Fibonacci series is 715 then, what is the 12th term of that series?a)157b)142c)144d)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A series in which any term is the sum of the preceding two terms is called a Fibonacci series. The first two terms are given initially and together they determine the entire series. If the difference of the squares of the ninth and the eighth terms of a Fibonacci series is 715 then, what is the 12th term of that series?a)157b)142c)144d)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer?.
A series in which any term is the sum of the preceding two terms is called a Fibonacci series. The first two terms are given initially and together they determine the entire series. If the difference of the squares of the ninth and the eighth terms of a Fibonacci series is 715 then, what is the 12th term of that series?a)157b)142c)144d)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A series in which any term is the sum of the preceding two terms is called a Fibonacci series. The first two terms are given initially and together they determine the entire series. If the difference of the squares of the ninth and the eighth terms of a Fibonacci series is 715 then, what is the 12th term of that series?a)157b)142c)144d)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A series in which any term is the sum of the preceding two terms is called a Fibonacci series. The first two terms are given initially and together they determine the entire series. If the difference of the squares of the ninth and the eighth terms of a Fibonacci series is 715 then, what is the 12th term of that series?a)157b)142c)144d)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer?.
Solutions for A series in which any term is the sum of the preceding two terms is called a Fibonacci series. The first two terms are given initially and together they determine the entire series. If the difference of the squares of the ninth and the eighth terms of a Fibonacci series is 715 then, what is the 12th term of that series?a)157b)142c)144d)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
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