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In a certain sequence, the first term is -4, and every term
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16 Mar 2019, 10:26
16 Mar 2019, 10:26
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In a certain sequence, the first term is -4, and every term thereafter is defined by \(2 * |x| * \frac{1}{2}\), where x = preceding term. What is the sum of the first 300 terms?
A. It cannot be determined from the information given.
B. 0
C. 1186
D. 1192
E. 1200
A. It cannot be determined from the information given.
B. 0
C. 1186
D. 1192
E. 1200
Re: In a certain sequence, the first term is -4, and every term
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20 Mar 2019, 14:40
20 Mar 2019, 14:40
Expert Reply
First of all, we can multiply in any order. So:
\(2* |x| * \frac{1}{2} = |x| * 2 * \frac{1}{2} = |x| * 1 = |x|\)
So each term is just the absolute value of the term before it.
The first term is -4. Terms 2 to 300 are 4. So 299 terms are equal to 4, for a sum of 299*4 = 1196. The first term is -4, so the total sum is 1196 - 4 = 1192.
\(2* |x| * \frac{1}{2} = |x| * 2 * \frac{1}{2} = |x| * 1 = |x|\)
So each term is just the absolute value of the term before it.
The first term is -4. Terms 2 to 300 are 4. So 299 terms are equal to 4, for a sum of 299*4 = 1196. The first term is -4, so the total sum is 1196 - 4 = 1192.
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Re: In a certain sequence, the first term is -4, and every term
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20 Oct 2022, 07:50
20 Oct 2022, 07:50
Given that the first term is -4, and every term thereafter is defined by \(2 * |x| * \frac{1}{2}\), where x = preceding term. And we need to find What is the sum of the first 300 terms
Term 1, \(T_1\) = -4
Each term after \(T_1\) is given by \(2 * |x| * \frac{1}{2}\) = |x|, where x is the preceding term
\(T_2\) = | \(T_1\) | = | -4| = 4
( Watch this video to learn about the Basics of Absolute Value )
\(T_3\) = | \(T_2\) | = |4| = 4
Now, each term after this will be equal to 4 only as |4| = 4
=> Sum of first 300 terms = -4 + 4 + ... + 4 (-4 followed by 299 4's) = 4 + 4 + ... + 4 (298 4's) = 298 * 4 = 1192
So, Answer will be D
Hope it helps!
Watch the following video to learn How to Sequence problems
Term 1, \(T_1\) = -4
Each term after \(T_1\) is given by \(2 * |x| * \frac{1}{2}\) = |x|, where x is the preceding term
\(T_2\) = | \(T_1\) | = | -4| = 4
( Watch this video to learn about the Basics of Absolute Value )
\(T_3\) = | \(T_2\) | = |4| = 4
Now, each term after this will be equal to 4 only as |4| = 4
=> Sum of first 300 terms = -4 + 4 + ... + 4 (-4 followed by 299 4's) = 4 + 4 + ... + 4 (298 4's) = 298 * 4 = 1192
So, Answer will be D
Hope it helps!
Watch the following video to learn How to Sequence problems
