Answer:
a. 21, ., ., 89
b. the sequence is 12, 13,25,38,63,101,164,265,429,
Step-by-step explanation:
The Fibonacci Sequence is regarded as a Rule whereby xₙ = xₙ₋₁+ xₙ₋₂
where:
xₙ is the number of terms "n"
xₙ₋₁ is the previous term (n-1)
xₙ₋₂ is the term before that (n-2)
(n) 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th 11th
x₁ x₂ x₃ x₄ x₅ x₆ x₇ x₈ x₉ x₁₀ x₁₁
xₙ 1 1 2 3 5 8 13 21 (21+13) 21+(21+13)
34 21+34=55
for the sequence 1,1,2,3,5,8,13,...........
a.) the next term of the sequence is the 8th number
following the rule = xₙ = xₙ₋₁+ xₙ₋₂
equate the n as the 8th term
x₈ = x₈₋₁+ x₈₋₂
x₈ = x₇+ x₆ = 13 + 8 = 21
the eleventh term of the sequence is x₁₁
x₁₁ = x₁₁₋₁+ x₁₁₋₂
x₁₁ = x₁₀+ x₉ = 55+34 = 89
B. i will choose 12,13 as an open end set, the next 7 terms will be
first term = 12
second term = 13
third term = 12+13= 25
fourth term = 25+13=38
fifth term = 38+25 = 63
sixth term = 63+38 = 101
seventh term = 101+63 = 164
eight term = 164+101 = 265
ninth term = 265+164 = 429
the sequence is 12, 13,25,38,63,101,164,265,429,
