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Math Help - Arithmetic sequence

  1. #1
    Member Rimas's Avatar
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    Arithmetic sequence

    ,IN the arithmetic sequence 17,a,b,c,41 what is the value of b?
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  2. #2
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    Hello, Rimas!

    You can baby-talk your way through this one . . .


    In the arithmetic sequence: 17,\,a,\,b,\,c,\,41, what is the value of b ?

    In an arithmetic sequence, the terms are "equally spaced".
    Since the distance from the first to last is 24, they must be 6 units apart.

    . . . . . . . . . 17\qquad\; a\qquad\;\: b \qquad\;\; c\qquad\;\, 41
    We have: .  - + - - + - - + - - + - - + -
    . . . . . . . . . . . \underbrace{\qquad}_6\;\;\;\underbrace{\qquad}_6\;  \;\;\underbrace{\qquad}_6\;\;\;\underbrace{\qquad}  _6

    Got it?

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  3. #3
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    Quote Originally Posted by Rimas View Post
    ,IN the arithmetic sequence 17,a,b,c,41 what is the value of b?
    The 5th term, 41 is:
    17+4k=41
    Thus,
    4k=24
    Thus,
    k=6
    That means the 3rh term, b, is:
    b=17+2\cdot 6=17+12=29
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