Practice Test Geeks(TMUA) Test of Mathematics for University Admission Practice Test
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Sequences & Series Flashcards

7 cards from real TMUA practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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  1. The first term of an arithmetic sequence is 3 and the common difference is 5. What is the 10th term?

    Answer: 48

    The nth term of an arithmetic sequence is a + (n-1)d = 3 + 9×5 = 48.

  2. In a geometric sequence, the first term is 2 and the common ratio is 3. What is the 5th term?

    Answer: 162

    The nth term of a geometric sequence is ar^(n-1) = 2 × 3^4 = 2 × 81 = 162.

  3. What is the sum of the first 20 terms of an arithmetic series with first term 4 and common difference 3?

    Answer: 650

    S_n = n/2 × (2a + (n-1)d) = 20/2 × (8 + 57) = 10 × 65 = 650.

  4. Which of the following sequences is arithmetic?

    Answer: 5, 8, 11, 14, ...

    5, 8, 11, 14 has a constant common difference of 3, making it arithmetic.

  5. The nth term of a sequence is given by T_n = 2n² − n + 1. What is the value of T_4?

    Answer: 29

    T_4 = 2(4²) − 4 + 1 = 32 − 4 + 1 = 29.

  6. A geometric series has first term 100 and common ratio 0.5. What is the sum to infinity?

    Answer: 200

    S∞ = a/(1 − r) = 100/(1 − 0.5) = 100/0.5 = 200.

  7. In an arithmetic sequence, the 5th term is 17 and the 9th term is 33. What is the common difference?

    Answer: 4

    From a + 4d = 17 and a + 8d = 33, subtracting gives 4d = 16, so d = 4.