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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=99, then what is a_20?

 

Thanks in advance. 

 Aug 22, 2020
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99 = F + 18D..............................(1)
19/2 * [2F + 18D] = 99................(2), solve for F, D

 

F = - 1683 / 19 - This is the first term
D =  198 / 19 - This is the common difference

 

20th term = - 1683 / 19 + [(198 / 19)*19]
20th term =2079 / 19

 Aug 22, 2020

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