Question

Determine the pattern in the successive sums from
the previous question. What will be the sum of
Fib (1) + Fib(2) + + Fib(10)?

pls answer correctly \(•.•)/​

Answer 1

Step-by-step explanation:

the tenth Fibonacci number is Fib(10) = 55. The sum of its digits is 5+5 or 10 and that is also the index number of 55 (10-th in the list of Fibonacci numbers).

Answer 2

Given : Fib(n) be the nth term of the Fibonacci sequence, with Fib(1)=1,Fib(2)=1,Fib(3)=2

To Find : Fib (1) + Fib(2) + + Fib(10)

Solution:

Fibonacci

a₁ = 1

a₂ = 1

aₙ =  aₙ₋₁   + aₙ₋₂

1  , 1 , 2,  3, 5, 8,  13, 21 ,  34,  55 , 89 , 144and so on

Sum of 1st two terms  = 1 + 1  = 2   =  3 - 1  = Fourth term - 1

Sum of 1st three terms  = 1 + 1  + 2 = 4   =  5 - 1  = Fifth term - 1

Sum of 1st four terms  = 1 + 1  + 2 + 3= 7  =  8 - 1  = Sixth term - 1

Hence

Sum of 1st n terms  = (n + 2)th term  -  1

Sum of 1st  10  terms  = (10 + 2)th term  -  1

=>Sum of 1st  10  terms  =12th term  -  1

Fib (1) + Fib(2) + + Fib(10) = Fib(12) - 1

= 144 - 1

= 143

Fib (1) + Fib(2) + + Fib(10)  = Fib(12) - 1  = 143  

 

Verification :

1 +1+ 2+ 3+ 5+8+ 13+ 21+ 34+ 55   = 143

Learn More:

Fibonacci अनुक्रम निम्नलिखित रूप में परिभाषित है

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प्रथम पाँच पद लिखिये, जिनका n वाँ पद दिया गया है ।

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