Write the terms a 1 </msub> , a 2 </msub> , a 3 </msub>

Davin Fields

Davin Fields

Answered question

2022-05-19

Write the terms a 1 , a 2 , a 3 , and a 4 of the following sequence. If the sequence converges, make a conjecture about its limit.
a n + 1 = 10 a n 1 ; a 0 = 0

Answer & Explanation

Kaelyn Barrett

Kaelyn Barrett

Beginner2022-05-20Added 5 answers

Given:
a n + 1 = 10 a n 1 , a 0 = 0

Substitute n = 0 , 1 , 2 , 3 and use the values of previous terms.
a 1 = 10 a 0 1 = 10 ( 0 ) 1 = 1
a 2 = 10 a 1 1 = 10 ( 1 ) 1 = 11
a 3 = 10 a 2 1 = 10 ( 11 ) 1 = 111
a 4 = 10 a 3 1 = 10 ( 111 ) 1 = 1111

Since the terms of the sequence decreases without bound and approaches , therefore the sequence diverges.

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