8=56
7=42
6=30
5=20
3=?
in Algebra 1 Answers by

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1 Answer

Look at the numbers on the rhs.

56     42     30     20   --- the members of this sequence are: a1, a2, a3, a4

    -14     -12    -10     --- here are the 1st differences: a_n - a_(n-1)

          2        2           --- here are the 2nd differences: b_n - b_(n-1)

Since the 2nd differences are constant, then we have a sequence of mathematically defined memebers. We could now work out the formula for generating the members of this sequence, but it will be faster and easier to work out manually the next few members to find the value for a6, which is when the lhs = 3.

The 2nd differences increase by 2 each time. This gives the 1st differences as:

-14   -12   -10   -8   -6

So now we can add on these 1st differences to the initial members of the sequence to get a5, a6, etc.

56      42     30      20    12     6   --- the members of the sequence are: a1, a2, a3, a4, a5, a6
    -14     -12    -10     -8     -6     --- here are more of the 1st differences: a_n - a_(n-1)

Answer: (when lhs = 3) is: 6

by Level 11 User (81.5k points)

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