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The sequence a1, a2, a3, …, an is defined by an = 9 + an – 1
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30 Jul 2018, 10:15
30 Jul 2018, 10:15
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The sequence \(a_1, a_2, a_3, ....,\) an is defined by \(a_n = 9 + a_{n – 1}\) for each integer n ≥ 2. If \(a_1 = 11\), what is the value of \(a_{35}\)?
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317
Re: The sequence a1, a2, a3, …, an is defined by an = 9 + an – 1
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03 Aug 2018, 09:26
03 Aug 2018, 09:26
1
We are looking to find the value of 35th integer.
We know the value of first term=11
There remains 34 more. Each term after 1st increases by 9 hence the 35th term is given by 11+ 34*9 = 317
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We know the value of first term=11
There remains 34 more. Each term after 1st increases by 9 hence the 35th term is given by 11+ 34*9 = 317
Posted from my mobile device
Re: The sequence a1, a2, a3, …, an is defined by an = 9 + an – 1
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12 Aug 2018, 07:03
12 Aug 2018, 07:03
Expert Reply
Explanation
Each term in the sequence is 9 greater than the previous term. To make this clear, write a few terms of the sequence: 11, 20, 29, 38, etc.
\(a_{35}\) comes 34 terms after \(a_1\) in the sequence. In other words, \(a_{35}\) is \(34 \times 9 = 306\) greater than \(a_1\).
Thus, \(a_{35} = 11 + 306 = 317\).
Each term in the sequence is 9 greater than the previous term. To make this clear, write a few terms of the sequence: 11, 20, 29, 38, etc.
\(a_{35}\) comes 34 terms after \(a_1\) in the sequence. In other words, \(a_{35}\) is \(34 \times 9 = 306\) greater than \(a_1\).
Thus, \(a_{35} = 11 + 306 = 317\).
