SOLUTION: The tenth term of an arithmetic sequence is 20 and the fifth term is 0. Find the sum of the terms from the eighth to the eighteenth, inclusive. Please help! Thank you!

Algebra ->  Sequences-and-series -> SOLUTION: The tenth term of an arithmetic sequence is 20 and the fifth term is 0. Find the sum of the terms from the eighth to the eighteenth, inclusive. Please help! Thank you!      Log On


   

Question 878423: The tenth term of an arithmetic sequence is 20 and the fifth term is 0. Find the sum of the terms from the eighth to the eighteenth, inclusive.
Please help! Thank you!
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
A%5Bn%5D=A0%2B%28n-1%29R
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A%5B10%5D=A0%2B%2810-1%29R
A0%2B9R=20
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A%5B5%5D=A0%2B%285-1%29R
A0%2B4R=0
Subtract these two terms,
A0%2B9R-A0-4R=20-0
5R=20
R=4
Then,
A0%2B4%284%29=0
A0=-16
So,
A%5Bn%5D=-16%2B4%28n-1%29
A%5Bn%5D=-16%2B4n-4
A%5Bn%5D=4n-20
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sum%28A%5Bn%5D%2C1%2CN%29=sum%28%284n-20%29%2Cn=1%2CN%29
sum%28A%5Bn%5D%2C1%2CN%29=4%2Asum%28n%2Cn=1%2CN%29%2BN%28-20%29
sum%28A%5Bn%5D%2C1%2CN%29=4%2A%28N%28N%2B1%29%2F2%29%2BN%28-20%29
sum%28A%5Bn%5D%2C1%2CN%29=2N%28N%2B1%29-20N
sum%28A%5Bn%5D%2C1%2CN%29=2N%5E2%2B2N-20N
S%5BN%5D=sum%28A%5Bn%5D%2C1%2CN%29=2N%5E2-18N
S%5B18%5D=2%2818%29%5E2-18%2A18
S%5B18%5D=324
S%5B7%5D=2%287%29%5E2-18%287%29
S%5B7%5D=98-126
S%5B7%5D=-28
So the the sum of the terms from 8th to 18th is,
S=S%5B18%5D-S%5B7%5D=324-%28-28%29=352