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A sequence of positive real numbers a_1, a_2, a_3... has the property that for i>=2, each a_i is equal to the sum of all the previous terms. If a_19=91, then what is a_20?

 Feb 16, 2021
 #1
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a_20 = 84.

 Feb 16, 2021
 #2
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The summation for n = 19 is usually 190

   this sequence is only 91

 

190x =91

x = 91/190    so the numbers in the sequence are reduced by this multiplier

 

\( \sum_{1}^{20} ( 91/190) n = 100.578947368\)           This would be   a20

 Feb 16, 2021

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