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Determine whether each sequence is arithmetric or geometric. Find the next three terms.

1.14, 19, 24, 29,...

geo, 34, 39, 44****

arithmetric, 32,36,41****

arithmetric, 34, 39, 44

The sequence is neither geo nor arith

2.-4,8,-16,32,...

arith, 64, 128, 256****

geo, -64, 128, -256****

geo, -48, 64, -80

The sequence is neither geo nor arith

3.81, 27, 9, 3,...

arith, 0, -3, -6

geo, 0, -3, -6****

geo, 1, 1/3, 1/9****

The sequence is neither geo nor arith

Find the next three terms in the sequence.

4. 3,12,21,30,...

40,50,60

38,46,54****

39,48,57

36,32,39****

5. 30,22,14,6

3,-12,-21****

-1,-8,-15

-1,-2,3

-2,-10,-18****

I PICKED 2 ANSWERS BECAUSE I THOUGHT THEY WERE BOTH RIGHT.

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  1. Very few sequences can be both arithmetic and geometric:

    a,a,a,a,...
    has d=0, r=1

    to be arithmetic, the difference between two terms must be constant

    to be arithmetic, the ratio between two terms must be constant

    For #1, 14, 19, 24, 29
    it is clear that you add 5 to each term to get the next. So, it is arithmetic, and the next terms are 34,39,44,49,...

    For #2, -4,8,-16,32
    you multiply by -2 each time, so it is geometric, and the next terms are -64,128,-256,...

    Take a look at the others and decide which they are. None will be both arithmetic and geometric.

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