Can someone tell me how to find the sum of the first 10 terms in the Fibonacci sequence with out adding...?

Answer 1

LET THE SERIES BE = 0,1,1,2,3,5,8,......,n,m
AND WE NEED TO FIND THE SUM OF FIBO. NOS. TILL m
THEN LETS FIRST CONSIDER
1,1,2,2+1,2(2)+1,3(2)+2(1)
WE OBSERVE THAT F(n+2) = 2{F(n)} + 1{F(n-1)}
THE SUM OF FIBO NOS. TILL m CAN BE GIVEN = F(n+2)-1
BY THE COMBINING THE FORMULAS WE GET:
S(0,1,1,2,3,5,8,......,n,m) = 2(m) + n -1
THERFORE
S(0,1,1,2,3,5,8,13,21,34) = 2(34) + 21 - 1
= 68 + 21 - 1
= 89-1
= 88

Answer 2

S(1) = Sum ( 1 ) = 1
S(2) = Sum ( 1, 1 ) = 2
S(3) = Sum ( 1, 1, 2 ) = 4
S(4) = Sum ( 1, 1, 2, 3 ) = 7
S(5) = Sum ( 1, 1, 2, 3, 5 ) = 12
S(6) = Sum ( 1, 1, 2, 3, 5, 8 ) = 20
S(7) = Sum ( 1, 1, 2, 3, 5, 8, 13 ) = 33
S(8) = Sum ( 1, 1, 2, 3, 5, 8, 13, 21 ) = 54
S(9) = Sum ( 1, 1, 2, 3, 5, 8, 13, 21, 34 ) = 88
S(10) = Sum ( 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 ) = 143
etc.

Notice how S(n) = F(n+2) - 1
So:
S(10) = F(12) - 1

That would be the 12th fibonacci number minus 1.
F(12) = 144
So:
S(10) = 143

You can also use Binet's formula (closed form) to calculate F(n).

Take the golden ratio: Φ = (1 + √5)/2 ≈ 1.618...

F(n) = round ( Φⁿ / √5 )
F(12) = round ( 1.618^12 / sqrt(5) )
F(12) = 144

So:
S(n) = round [ Φ^(n+2) / √5 ] - 1
S(10) = round [ 1.618^12) / √5 ] - 1
S(10) = 143

Answer 3

Since 1+10=11, 2+9=11... & you started with an odd number & ended w/ an even (1-10), do (half of ten) times 11, aka 5x11=55. Any other math questions that are Alg. 1 or beginning geometry & down, feel free to email me @ my nickname! :)

Answer 4

just arrange the numbers in order Ex: 10 14 24 38

Answer 5

for one thing to get a sum is to add so i looked up this...

http://encyclopedia.thefreedictionary.com/Fibonacci+


hope it helps. LOL

Answer 6

Is it that difficult to add just 10 numbers?

Answer 7

you're able to use a formulation obtained by using fixing the version equation: f(n) = f(n-one million) + f(n-2), f(one million)=one million and f(2)=one million . the answer is: f(n) = ((one million+sqrt(5))/2)^n/sqrt(5) - ((one million-sqrt(5))/2)^n/sqrt(5) grotesque? sure! you ought to apply a scientific calculator... or ... utility like Maple or Matlab... or Excel formulation.

Answer 8

Yeah, click here to get the answer

http://en.wikipedia.org/wiki/Fibonacci_sequence

Answer 9

I sure can't!