Explain why cos(x)=sin(90-x) for x such that 0
1 answer:
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Answer:
The correct answer is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89.
Step-by-step explanation:
In a study of the progeny of rabbits, Fibonacci encountered the sequence now bearing his name.
The sequence is defined recursively as:
=
+
, where a1 = 1 and a2 = 1 where n is a natural number.
For n = 0 ; a2 = a0 + a1
⇒ a0 = 0.
For n = 1 ; a3 = a1 + a2 = 1+1
⇒ a3 = 2.
For n = 2 ; a4 = a2 + a3 = 1+2
⇒ a4 = 3.
For n = 3 ; a5 = a3 + a4 = 2+3
⇒ a3 = 5.
For n = 4 ; a6 = a4 + a5 = 3+5
⇒ a6 = 8.
For n = 5 ; a7 = a5 + a6 = 5+8
⇒ a7 = 13.
For n = 6 ; a8 = a6 + a7 = 8+13
⇒ a8 = 21.
For n = 7 ; a9 = a7 + a8 = 21+13
⇒ a9 = 34.
For n = 8 ; a10 = a8 + a9 = 21+34
⇒ a10 = 55.
For n = 9 ; a11 = a9 + a10 = 55+34
⇒ a11 = 89.
Thus the first 12 terms of fibonacci sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89.