Arithmetico-Geometric Progression

38 MCQs This test covers the A.G. sequence and series, the nth term, the sum to n terms and the sum to infinity, including the condition |r| < 1.

MCQs

38 questions · 30 min · 38 marks

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Sample questions

The first 5 of 38. Try each one, then tap to see the answer.

  1. Question 1

    The sequence formed by multiplying the corresponding terms of an A.P. and a G.P. is called

    • Aharmonic sequence
    • Barithmetico-geometric sequence
    • Cgeometric series
    • Darithmetic mean
    Show answer

    Answer: B

    That product sequence is arithmetico-geometric.

  2. Question 2

    The nth term of the arithmetico-geometric sequence formed from the A.P. a, a + d, a + 2d, ... and the G.P. b, br, br^2, ... is

    • A{a + (n - 1)d}br^(n-1)
    • B(a + nd)br^n
    • C{a + (n - 1)d} + br^(n-1)
    • Dabdr^(n-1)
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    Answer: A

    The nth term is the nth term of the A.P. times the nth term of the G.P.

  3. Question 3

    The sum of the terms of an arithmetico-geometric sequence is called an

    • Aarithmetic series
    • Bgeometric series
    • Carithmetico-geometric series
    • Dharmonic series
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    Answer: C

    Summing the terms of the sequence gives the arithmetico-geometric series.

  4. Question 4

    The nth term of the A.P. 1, 4, 7, ... is

    • A3n + 1
    • B4n - 3
    • Cn + 3
    • D3n - 2
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    Answer: D

    a_n = 1 + (n - 1)3 = 3n - 2.

  5. Question 5

    The nth term of the G.P. 5, 10, 20, ... is

    • A5(2)^(n-1)
    • B5(2)^n
    • C2(5)^(n-1)
    • D10(2)^(n-1)
    Show answer

    Answer: A

    b_n = 5(2)^(n-1).

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