## Step By Step Answers Example

**
1)**

20
n=2 | -3+3(n-1) |

We could plug in all the numbers between 2 and 20 to get: 0+3+6+9+12+15+18+21+24+27+30+33+36+39+42+45+48+51+54

And then add them all together**OR**

We plug in n=2 to get a_{2}=0

We plug in n=20 to get a_{20}=54

The number of terms, k = 20-2+1 so k=19

Then we use the formula ^{k}/_{2}(a_{2}+a_{20}) to get: 513

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**2)** 8
n=-1 | 7+3(n-1) |

We could plug in all the numbers between -1 and 8 to get: 1+4+7+10+13+16+19+22+25+28

And then add them all together**OR**

We plug in n=-1 to get a_{-1}=1

We plug in n=8 to get a_{8}=28

The number of terms, k = 8-^{-}1+1 so k=10

Then we use the formula ^{k}/_{2}(a_{-1}+a_{8}) to get: 145

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**3)** 16
n=3 | -10+(n-1) |

We could plug in all the numbers between 3 and 16 to get: -8+-7+-6+-5+-4+-3+-2+-1+0+1+2+3+4+5

And then add them all together**OR**

We plug in n=3 to get a_{3}=-8

We plug in n=16 to get a_{16}=5

The number of terms, k = 16-3+1 so k=14

Then we use the formula ^{k}/_{2}(a_{3}+a_{16}) to get: -21

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**4)** 13
n=4 | 4+^{4}/_{3}(n-1) |

We could plug in all the numbers between 4 and 13 to get: 8+^{28}/_{3}+^{32}/_{3}+12+^{40}/_{3}+^{44}/_{3}+16+^{52}/_{3}+^{56}/_{3}+20

And then add them all together**OR**

We plug in n=4 to get a_{4}=8

We plug in n=13 to get a_{13}=20

The number of terms, k = 13-4+1 so k=10

Then we use the formula ^{k}/_{2}(a_{4}+a_{13}) to get: 140

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