Question 211735
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