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Flashcards · Maths · Algebra

Sequences and the nth Term

18 cards

  1. What is a term-to-term rule?

    A rule that tells you how to get from one term to the next, such as add 3.

  2. What is the position-to-term rule?

    The nth term: a formula that gives any term from its position \(n\), such as \(3n + 2\).

  3. What is an arithmetic sequence?

    A sequence that goes up or down by the same amount each time, called the common difference.

  4. What is a geometric sequence?

    A sequence where each term is multiplied by the same number, such as 3, 6, 12, 24.

  5. What is a Fibonacci-type sequence?

    A sequence in which each term is the sum of the two terms before it.

  6. What are the first five triangular numbers?

    1, 3, 6, 10 and 15.

  7. How do you find the nth term of a linear sequence?

    The common difference \(d\) gives \(dn\). Compare \(dn\) with the terms and adjust. For 5, 8, 11 it is \(3n + 2\).

  8. What is the nth term of 4, 7, 10, 13?

    \(3n + 1\).

  9. What is the nth term of 20, 17, 14, 11?

    \(-3n + 23\).

  10. How do you test whether a number is in a sequence?

    Set the nth term equal to the number and solve. If \(n\) is not a positive whole number, it is not in the sequence.

  11. Is 100 a term of \(3n + 2\)?

    No. \(3n = 98\) gives \(n = 32.67\ldots\), which is not a whole number.

  12. How do you find the first term of \(3n + 2\) that is over 100?

    \(3n + 2 > 100\) gives \(n > 32.67\ldots\), so \(n = 33\) and the term is 101.

  13. How do you check an nth term?

    Substitute \(n = 1\) and \(n = 2\) and see whether you get the first two terms.

  14. What is the nth term for a row of squares made from matchsticks (4, 7, 10, ...)?

    \(3n + 1\). Three sticks are added for each new square, plus one to start.

  15. How do you spot a quadratic sequence?

    The first differences change, but the second differences are constant.

  16. A quadratic sequence has second difference 2. What does its nth term start with?

    \(n^2\), because the coefficient is half the second difference (Higher tier).

  17. What is the nth term of 4, 10, 18, 28, 40 (Higher tier)?

    \(n^2 + 3n\).

  18. What is the nth term of a geometric sequence (Higher tier)?

    \(ar^{n-1}\), where \(a\) is the first term and \(r\) the common ratio. For 3, 6, 12 it is \(3 \times 2^{n-1}\).