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Question 1

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easy

[Maximum mark: 6]

Consider an arithmetic sequence 2,6,10,14,2,6,10,14,\dots

  1. Find the common difference, dd. [2]

  2. Find the 1010th term in the sequence. [2]

  3. Find the sum of the first 1010 terms in the sequence. [2]

easy

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Question 2

calculator

easy

[Maximum mark: 6]

The table shows the first four terms of three sequences: unu_n, vnv_n, and wnw_n.

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  1. State which sequence is

    1. arithmetic;

    2. geometric. [2]

  2. Find the sum of the first 5050 terms of the arithmetic sequence. [2]

  3. Find the exact value of the 1313th term of the geometric sequence. [2]

easy

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Question 3

calculator

hard

[Maximum mark: 7]

  1. Write down the quadratic expression 3x2+5x23x^2 + 5x - 2 in the form (axb)(x+c)(ax-b)(x+c).[2]

  2. Hence, or otherwise, find the coefficient of the term in x9x^9 in the expansion
    of (3x2+5x2)5(3x^2+5x-2)^5. [5]

hard

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