Ask Question
2 March, 19:21

Consider the sequence defined recursively by an+1 = (an - 1 if an ≥ 10 2an if an < 10)

(a) Let a0 be equal to the last digit in your student number, and compute a1, a2, a3, a4.

(b) Suppose an = 1, and find an+4.

(c) If a0 = 3, does limn→[infinity] an exist?

+5
Answers (1)
  1. 2 March, 21:30
    0
    a) a₁ = 14, a₂ = 13, a₃ = 12, a₄ = 11

    b) an+4 = 16

    c) Does not exist

    Step-by-step explanation:

    The last digit in student number is given as 7.

    a) a₀ = 7

    Since an < 10 we use 2an

    Therefore a₁ = a₀₊₁ = 2 * a₀ = 2 * 7 = 14

    a₂ = a₁₊₁ = a₁ - 1 = 14 - 1 = 13

    a₃ = a₂₊₁ = a₂ - 1 = 13 - 1 = 12

    a₄ = a₃₊₁ = a₃ - 1 = 12 - 1 = 11

    b) an = 1, we have an+1 = 2an

    Therefore an+2 = an+1+1 = 2 * 2 = 4

    an+3 = an+2+1 = 2 * 4 = 8

    an+4 = an+3+1 = 2 * 8 = 16

    Therefore, an+4 = 16

    c) If a₀ = 3, therefore a₁ = a₀₊₁ = 2*3 = 6

    a₂ = a₁₊₁ = 2*6 = 12

    a₃ = a₂₊₁ = a₂₋₁ = 12 - 1 = 11

    a₄ = a₃₊₁ = a₃₋₁ = 11 - 1 = 10

    a₅ = a₄₊₁ = a₄₋₁ = 10 - 1 = 9

    a₆ = 2*9 = 18

    We can therefore see that limn→[infinity] does not exist.
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “Consider the sequence defined recursively by an+1 = (an - 1 if an ≥ 10 2an if an < 10) (a) Let a0 be equal to the last digit in your ...” in 📘 Mathematics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers