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 \(•.•)/
Answers
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).
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
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