SOLUTION: pls. help 10,7,4....to 15th terms �Write the next 3 terms, �Find the indicated tn, �Find the indicated Sn.

Question 211735This question is from textbook COLLEGE ALGEBRA
: pls. help
10,7,4....to 15th terms
�Write the next 3 terms,
�Find the indicated tn,
�Find the indicated Sn.

This question is from textbook COLLEGE ALGEBRA

Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
10,7,4,.......
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This appears to be an arithmetic series with rule,,,,-3,,,between terms
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The form of the series is ,,,a(n) = a(1) + (n-1)d,,,with a(1) =10, d=(-3)
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check,,1st term, a(1) = 10 +(n-1)(-3) = 10,,,ok
,,,,,,,2nd term,,, a(2) =10 +(2-1)(-3) = 7,,,,ok
,,,,,,,3rd term,,, a(3) =10 +(3-2)(-3) = 4,,,,ok
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,,,,,,,,,,,,,,,,,,,,a(15) = 10 +(15-1)(-3) = -32,,,,,,answer
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The sum of an arithmetic series is the average * number of terms.
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S = n ( {a(1) +a(n)} /2 )
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S(15) = (15) * { 10 + (-32) } /2 = (15) * (-11) = - 165
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check,,,10,7,4,1,-2,-5,-8,-11,-14,-17,-20,-23,-26,-29,-32
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15 th term is indeed (-32), and sum is (-165),,,ok
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