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    arithmetic and geometric progression , classical problem

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    I need assistance in discerning sequences and series including the classical grains and checkboard problem

    © BrainMass Inc. brainmass.com March 4, 2021, 6:51 pm ad1c9bdddf
    https://brainmass.com/math/algebraic-geometry/arithmetic-geometric-progression-classical-problem-65625

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    1) Use the arithmetic series of numbers 1, 3, 5, 7, 9,...to find the following:
    a) What is d, the difference between any 2 terms?
    Answer:
    The difference between any two terms = ( n+1 )th term - ( n )th term

    Hence , difference , d = 3-1 = 5-3 = 7-5 = 2

    Answer d = 2

    b) Using the formula for the nth term of an arithmetic series, what is 101st term? Answer:
    nth term=a+(n-1)d..............(1)
    Given a=first term=1
    n=101
    d=2
    putting above values in formula 1
    nth term=1+(101-1)*2
    =1+200=201
    Therefore , nth term = 201

    Using the formula for the sum of an arithmetic series, what is the sum of the first 20 terms?
    Answer:

    formula for the sum of an arithmetic series=n/2(2a +(n-1)d)..............(1)
    given that , n = 20
    a = first term = 1
    Therefore , sum = 20/2(2*1+19*2)
    =10*(40)
    sum = 400

    Using the formula for the sum of an arithmetic series, what is the sum of the first 30 terms?
    Answer:
    formula for the sum of an arithmetic series=n/2(2a +(n-1)d)..............(1)
    given that n = 30
    a = first term =1
    = 30/2(2*1+29*2)
    ...

    Solution Summary

    The solution contains answers to various questions involving A.P and G.P concepts including the famous classical problem involving checkboard and grains.

    $2.49

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