Question 482605
Descibe pattern. Then write the next three numbers.

1) 640,320,160,80...
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Take half of 640, get 320
Take half of 320, get 160
Take half of 160, get 80
So,
Take half of 80, get 40
Take half of 40, get 20
Take half of 20, get 10

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2) 4,12,36,108...
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Multiply 4 by 3, get 12
Multiply 12 by 3, get 36
Multiply 35 by 3, get 108
So,
Multiply 108 by 3, get 324
Multiply 324 by 3, get 972
Multiply 972 by 3, get 2916

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3) 1,1,2,3,5,8...
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To get the <font color="red">3</font>rd term, add the <font color="red">1</font>st and <font color="red">2</font>nd, get 1+1=2
To get the <font color="red">4</font>th term, add the <font color="red">2</font>nd and <font color="red">3</font>rd, get 1+2=3
To get the <font color="red">5</font>th term, add the <font color="red">3</font>rd and <font color="red">4</font>th, get 2+3=5
So
To get the <font color="red">6</font>th term, add the <font color="red">4</font>th and <font color="red">5</font>th, get 3+5=8
To get the <font color="red">7</font>th term, add the <font color="red">5</font>th and <font color="red">6</font>th, get 5+8=13
To get the <font color="red">8</font>th term, add the <font color="red">6</font>th and <font color="red">7</font>th, get 8+13=21

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4) 2,11,38,119...
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To get the <font color="red">1</font>st term,
1. multiply <font color="red">1</font> by 6, get <font color="red">1</font>×6 = 6
2. Subtract that from 27, get 27-6 = 21,
3. Multiply that by <font color="red">1</font>, get 21×<font color="red">1</font> = 21
4. Subtract that from 48, get 48-21 = 27
5. Multiply that by <font color="red">1</font>, get 27×<font color="red">1</font> = 27
6. Subtract 25 from that, get 27-25 = 2, the <font color="red">1</font>st term.

To get the <font color="red">2</font>nd term,
1. multiply <font color="red">2</font> by 6, get <font color="red">2</font>×6 = 12
2. Subtract that from 27, get 27-12 = 15,
3. Multiply that by <font color="red">2</font>, get 15×<font color="red">2</font> = 30
4. Subtract that from 48, get 48-30 = 18
5. Multiply that by <font color="red">2</font>, get 18×<font color="red">2</font> = 36
6. Subtract 25 from that, get 36-25 = 11, the <font color="red">2</font>nd term

To get the <font color="red">3</font>rd term,
1. multiply <font color="red">3</font> by 6, get <font color="red">3</font>×6 = 18
2. Subtract that from 27, get 27-18 = 9,
3. Multiply that by <font color="red">3</font>, get 9×<font color="red">3</font> = 27
4. Subtract that from 48, get 48-27 = 21
5. Multiply that by <font color="red">3</font>, get 21×<font color="red">3</font> = 63
6. Subtract 25 from that, get 63-25 = 38, the <font color="red">3</font>rd term

To get the <font color="red">4</font>th term,
1. multiply <font color="red">4</font> by 6, get <font color="red">4</font>×6 = 24
2. Subtract that from 27, get 27-24 = 3,
3. Multiply that by <font color="red"></font>, get 3×<font color="red">4</font> = 12
4. Subtract that from 48, get 48-12 = 36
5. Multiply that by <font color="red">4</font>, get 36×<font color="red">4</font> = 144
6. Subtract 25 from that, get 144-25 = 119, the <font color="red">4</font>th term

So,

To get the 5th term,
1. multiply <font color="red">5</font> by 6, get <font color="red">5</font>×6 = 30
2. Subtract that from 27, get 27-30 = -3,
3. Multiply that by <font color="red">5</font>, get -3×<font color="red">5</font> = -15
4. Subtract that from 48, get 48-(-15) = 48+15 = 63
5. Multiply that by <font color="red">5</font>, get 63×<font color="red">5</font> = 315
6. Subtract 25 from that, get 315-25 = 290, the <font color="red">5</font>th term

To get the <font color="red">6</font>th term,
1. multiply <font color="red">6</font> by 6, get <font color="red">6</font>×6 = 36
2. Subtract that from 27, get 27-36 = -9,
3. Multiply that by <font color="red">6</font>, get -9×<font color="red">6</font> = -54
4. Subtract that from 48, get 48-(-54) = 48+54 = 102
5. Multiply that by <font color="red">6</font>, get 102×<font color="red">6</font> = 612
6. Subtract 25 from that, get 612-25 = 587, the <font color="red">6</font>th term

To get the <font color="red">7</font>th term,
1. multiply <font color="red">7</font> by 6, get <font color="red">7</font>×6 = 42
2. Subtract that from 27, get 27-42 = -15,
3. Multiply that by <font color="red">7</font>, get -15×<font color="red">7</font> = -105
4. Subtract that from 48, get 48-(-105) = 48+105 = 153
5. Multiply that by <font color="red">7</font>, get 153×<font color="red">7</font> = 1071
6. Subtract 25 from that, get 1071-25 = 1046, the <font color="red">7</font>th term

Edwin</pre>