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Math Help - Arithmetic Progression help please

  1. #1
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    Arithmetic Progression help please

    In an arithmetic progression, the sum of the first ten terms is 50, and the fith term is three times the second term. Find:
    i) The first term
    ii) The sum of the first 20 terms
    Im having problems with finding the first term, I will be able to do the second part of the question easily, as its just the formula.

    My text book hasnt got any examples of this sort of question in it, so Im unsure how to go about trying to complete it.

    thanks
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  2. #2
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    Hello fishkeeper
    Quote Originally Posted by fishkeeper View Post
    Im having problems with finding the first term, I will be able to do the second part of the question easily, as its just the formula.

    My text book hasnt got any examples of this sort of question in it, so Im unsure how to go about trying to complete it.

    thanks
    With the usual notation, the sum of the first 10 terms is:
    5(2a + 9d) = 50

    \Rightarrow 2a+9d = 10
    ...(1)
    The second term is a + d; the fifth is a + 4d. So:
    a+4d=3(a+d)

    \Rightarrow 2a = d
    Substitute into (1):
    10d=10

    \Rightarrow d = 1

    \Rightarrow a = \tfrac12
    OK now?

    Grandad
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  3. #3
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    thanyou very much for a quick reply

    Its taken me a little while to work through what you wrote, but I think ive understood fairly well, I'll write out my interpretation on the second part.

    the a+ 4d: the 4d is the 4 terms that have each had the common ratio added onto them? And that equals 3 lots of a+d (the second term of the sequence as its had the common ratio added onto it?)

    thanks
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  4. #4
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    Hello fishkeeper
    Quote Originally Posted by fishkeeper View Post
    thanyou very much for a quick reply

    Its taken me a little while to work through what you wrote, but I think ive understood fairly well, I'll write out my interpretation on the second part.

    the a+ 4d: the 4d is the 4 terms that have each had the common ratio added onto them? And that equals 3 lots of a+d (the second term of the sequence as its had the common ratio added onto it?)

    thanks
    That's correct (although it's the common difference in an AP).

    Grandad
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