Rule and Next Three Terms?? Easy

Sequence: 20, 10, 5, 2.5....
Sequence: 0.1, -1, 10, -100...
Sequence: 1, 7, 19, 43...
Sequence: 12, 5, -2, -9,...
Sequence: 1, 0, -2, -6, -14...
Thanks:)

1) 20, 10, 5, 2.5, 1.25, 0.625, 0.3125....Each one is half the previous one.

2) 0.1, -1, -10, -100, -1000, -10000, -100000...Multiplied by -10

3) 1, 7, 19, 43, 91, 187, 379...Double the previous difference and add it 6, 12, 24, 48, 96, 192

4) 12, 5, -2, -9, -16, -23, -30.......-7 each time

5) 1, 0, -2, -6, -14, -30, 62, 126....minus 1, 2, 4, 8, 16, 32, 64.(doubling the number)

:-)

Hi Shammy,

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20, 10, 5, 2.5, ...

Rule:
T[n] = 5 * 2^(3 - n).

Next three terms:
T[5] = 5 * 2^(-2) = 5 * (1 / 4) = 5 / 4.
T[6] = 5 * 2^(-3) = 5 * (1 / 8) = 5 / 8.
T[7] = 5 * 2^(-4) = 5 * (1 / 16) = 5 / 16.

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1/10, -1, 10, -100, ...

Rule:
T[n] = (-1)^(n - 1) * 10^(n - 2).

Next three terms:
T[5] = (-1)^4 * 10^3 = 1 * 1,000 = 1,000.
T[6] = (-1)^5 * 10^4 = -1 * 10,000 = -10,000.
T[7] = (-1)^6 * 10^5 = 1 * 100,000 = 100,000.

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1, 7, 19, 43, ...

Rule:
T[n] = 3 * 2^(n) - 5.

Next three terms:
T[5] = 3 * 2^5 - 5 = 3 * 32 - 5 = 96 - 5 = 91.
T[6] = 3 * 2^6 - 5 = 3 * 64 - 5 = 192 - 5 = 187.
T[7] = 3 * 2^7 - 5 = 3 * 128 - 5 = 384 - 5 = 379.

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12, 5, -2, -9, ...

Rule:
T[n] = 19 - 7n.

Next three terms:
T[5] = 19 - 7 (5) = 19 - 35 = -16.
T[6] = 19 - 7 (6) = 19 - 42 = -23.
T[7] = 19 - 7 (7) = 19 - 49 = -30.

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1, 0, -2, -6, -14, ...

Rule:
T[n] = 2 - 2^(n - 1).

Next three terms:
T[5] = 2 - 2^4 = 2 - 16 = -14.
T[6] = 2 - 2^5 = 2 - 32 = -30.
T[7] = 2 - 2^6 = 2 - 64 = -62.
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/2. 1.25, 0.625, 0.3125
*(-10). 1000, -10000, 100000
+(6*2^n). 91, 187, 379
-7. -16, -23, -30
-2^n. -30, -62, -126