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Math Help - find next term

  1. #1
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    find next term

    Given the sequence, what is the value of a?
    . . .3, 10, 31, a , 283, . .
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  2. #2
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    Hello, JoDan!

    Given the sequence, what is the value of a?
    . . 3,\:10,\:31,\:a,\;283, \cdots

    There isn't much to work with . . .

    The differences are: . 3\underbrace{\qquad}_7 10\underbrace{\qquad}_{21}31 \underbrace{\qquad}_? a \underbrace{\qquad }_? 283


    I conjectured that the differences are: . 7,\;7\!\cdot\!3,\;7\!\cdot\!3^2,\;7\!\cdot\!3^3

    . . and it worked!


    . . . . . 3\underbrace{\qquad}_7 10\underbrace{\qquad}_{21}31 \underbrace{\qquad}_{63} {\color{blue}94} \underbrace{\qquad }_{189} 283

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