Mathematics
prepretocue
19

The common ratio of a geometric series is 9, while the sum of the first 10 terms in the series is 435,848,050. What is the first term in the series?

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(1) Answers
CassKnight

s(sub n) =[a(sub 1) * (1 - r^n)] / (1 - r) n = 10 (10th term) r = 9 (common ratio) a(sub 1) = ? (first term in the sequence) s(sub n) = 435,484,050 (sum of the first 10 terms) 435,848,050 = [a (1 - 9^10)/(1-9)] 435,848,050 = [a ( 1 - 3,486,784,4010/-8) ] 435,848,050 = a (435,848,050) Divide both sides by 435,848,050 1 = a(sub 1) CHECK s(sub 10) = [1* (1 - 9^10)/1-9) ] s(sub 10) = [1* (435,848,050) ] s (sub 10) = 435,848,050

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