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Sequences and Series
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Sequences and Series

by: bellezamatematica
  1. 1

    Find the sum of the first one hundred odd numbers.

  2. 2

    How many terms of the arithmetic sequence 2 , 2.3 , 2.6 , 2.9 , ... must be taken before the terms exceed 100 ?

  3. 3

    Find x given that 3 - 6 + 12 - 24 + ... + x = - 63

  4. 4

    Find the common ratio and the general term of the sequence ab , a , a/b , a/(b^2)

  5. 5

    Find the number of terms in the geometric sequence 0.25 , 0.75 , 2.25 , ... , 44286.75

  6. 6

    The sum of the first eight terms of the sequence ln x , ln (x^2 y) , ln (x^3 y^2) , ... is given by 4 ( a ln x + b ln y ). Find a and b.

  7. 7

    When a ball is dropped onto a flat floor, it bounces to 65 % of the height from which it was dropped. If the ball is dropped from 80 cm, find the height of the fifth bounce.

  8. 8

    The sum of the first n terms of an arithmetic sequence is S = 3n^2 - 2n . Find the general term.

  9. 9

    The sum of three successive terms of a geometric sequence is 35/2 while their product is 125. Find the three terms.

  10. 10

    Consider the infinite geometric series 1 + ((2x) / 3) + ((2x) / 3) ^2 + ((2x) / 3) ^3 + ...For what values of x does the series converge ?

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