MATH

A new sequence is formed by adding together the corresponding terms of a geometric sequence and an arithmetric sequence. the geometric sequence has a common ratio of 3 and the arthmetric sequence has a common difference of -2.
The first two terms of the new sequence are 4 and 20.

how do you calculate the third term of the new sequence?

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  1. I will assume that you are adding the corresponding terms of each sequence, that is ..
    new sequence:
    t1 = a+a
    t2 = a+d + ar
    t3 = a+2d + ar^2
    etc

    so a+a = 4
    a+d + ar = 20
    but d=-2 and r=3

    2a = 4
    a = 2
    So all is known

    t3 = 2 - 4 + 2(9) = 16

    check:
    AS: 2, 0, -2, -4, ..
    GS: 2, 6, 18, 54, ..

    new sequence is :
    4, 6, 16 , 50 ..
    All looks good

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    posted by Reiny

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