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daktielti 2022-07-07 Answered
Write the terms a 1 , a 2 , a 3 , and a 4 of the following sequences. If the sequence appears to converge, make a conjecture about its limit. If the sequence diverges, explain why.
a n + 1 = 10 a n ; a 1 = 1
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Answers (1)

Alexis Fields
Answered 2022-07-08 Author has 14 answers
a n + 1 = 10 a n , a 1 = 1
We have to find a 2

Put n = 1
a 1 + 1 = 10 a 1
a 1 + 1 = 10 a 1
a 2 = 10

Put n = 2
a 2 + 1 = 10 a 2
a 3 = 10 10
a 3 = 1

Put n = 3
a 3 + 1 = 10 a 3
a 4 = 10 1
a 4 = 10

Thus, we get the sequence 1 , 10 , 1 , 10 , . . .
This sequence have two limit points {1,10}. And it is divergence sequence as for convergence sequence should be one limit point.

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