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2 marksNumber Sequences and Rules

CSEC Mathematics · Question 7(b)(iii)

The first 8 terms of another sequence with nth term, U(n), are 1, 1, 2, 3, 5, 8, 13, 21, where U(1) = 1, U(2) = 1 and U(n) = U(n-1) + U(n-2) for n ≥ 3. For example, U(5) = U(4) + U(3) = 3+2=5 and U(7) = U(6) + U(5) = 8+5=13.

Show that U(20) - U(19) = U(19) - U(17).

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Other parts of this question

  1. 7(a)(i)Show that the first term of the sequence is 1.[1 mark]
  2. 7(a)(ii)What is the third term of the sequence?[1 mark]
  3. 7(a)(iii)Given that T_n = 145, what is the value of n?[3 marks]
  4. 7(b)(i)Write down the next two terms in the sequence, that is, U(9) and U(10).[2 marks]
  5. 7(b)(ii)Which term in the sequence is the sum of U(18) and U(19)?[1 mark]

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