Find the next number in the sequence: 1, 1, 2, -1, 1, -2,-1,
Answers
Given : sequence: 1, 1, 2, -1, 1, -2,-1,
To Find : next number in the sequence
Solution:
1, 1, 2, -1, 1, -2,-1,
1 + 1 = 2
1 - 2 = - 1
2 + (-1) = 1
-1 - 1 = - 2
1 + (-2) = - 1
-2 - (-1) = - 1
Next number in sequence is - 1
logic is
Tₙ₊₂ = Tₙ + (-1)ⁿ⁺¹Tₙ₊₁ where T₁ = 1 T₂ = 1
n = 1 , T₃ = T₁ + (-1)¹⁺¹T₂ = 1 + 1 = 2
n = 2 T₄ = T₂ + (-1)²⁺¹T₃ = 1 - 2 = -1
n =3 T₅ = T₃ + (-1)³⁺¹T₄ = 2 + (-1) = 1
n =4 T₆ = T₄ + (-1)⁴⁺¹T₅ = -1 - (1) = -2
n =5 T₇ = T₅ + (-1)⁵⁺¹T₆ = 1 + (-2) = -1
n =6 T₈ = T₆ + (-1)⁶⁺¹T₇ = -2 - (-1) = -1
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Answer:
dcvncc
Step-by-step explanation: