Question

# A series in which any term is equal to the sum of the preceding two terms is called a Fibonacci series. Usually the first two terms are given initially and together they determine the entire series. Now, it is known that the difference of the squares of the ninth and the eighth terms of a Fibonacci series is 840. What is the 12th term of that series?

A
157
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B
142
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C
143
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D
Cannot be determined
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Solution

## The correct option is D Cannot be determinedLeta,b,a+b,a+2b,2a+3b.... be the Fibonacci series.(9thterm)2−(8thterm)2=840(13a+21b)2−(8a+13b)2=840105a2+338ab+272b2=840(5a+8b)(21a+34b)=84012thterm=55a+89bIfa=1,b=1(5a+8b)(21a+34b)=715Ifa=2,b=1(or)a=1,b=2(5a+8b)(21a+34b)>840It is not possible and 12thterm cannot be determined.

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