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In a certain sequence, the term an is defined by the formula
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27 Jul 2018, 01:32
27 Jul 2018, 01:32
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86% (01:06) correct
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In a certain sequence, the term an is defined by the formula \(a_n = a_{n – 1} + 10\) for each integer n ≥ 2. What is the positive difference between \(a_{10}\) and \(a_{15}\)?
(A) 5
(B) 10
(C) 25
(D) 50
(E) 100
(A) 5
(B) 10
(C) 25
(D) 50
(E) 100
Re: In a certain sequence, the term an is defined by the formula
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12 Aug 2018, 04:48
12 Aug 2018, 04:48
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Expert Reply
Explanation
This is an arithmetic sequence where the difference between successive terms is always +10.
The difference between, for example, \(a_{10}\) and \(a_{11}\), is exactly 10, regardless of the actual values of the two terms. The difference between \(a_{10}\) and \(a_{12}\) is \(10 + 10 = 20\), or \(10 \times 2 = 20\), because there are two “steps,” or terms, to get from \(a_{10}\) to \(a_{12}\). Starting from a10, there is a sequence of 5 terms to get to \(a_{15}\).
Therefore, the difference between \(a_{10}\) and \(a_{15}\) is \(10 \times 5 = 50\).
This is an arithmetic sequence where the difference between successive terms is always +10.
The difference between, for example, \(a_{10}\) and \(a_{11}\), is exactly 10, regardless of the actual values of the two terms. The difference between \(a_{10}\) and \(a_{12}\) is \(10 + 10 = 20\), or \(10 \times 2 = 20\), because there are two “steps,” or terms, to get from \(a_{10}\) to \(a_{12}\). Starting from a10, there is a sequence of 5 terms to get to \(a_{15}\).
Therefore, the difference between \(a_{10}\) and \(a_{15}\) is \(10 \times 5 = 50\).
Re: In a certain sequence, the term an is defined by the formula
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06 Mar 2020, 14:04
06 Mar 2020, 14:04
Why don't we use inclusive counting and get 60?
