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How do you solve this arithmetic series problem given first term is 9 common difference is -3 sum of the terms is 0 then find the number of terms?
Wiki User
∙ 11y ago
Te sequence is defined by
t(n) = 12 - 3n where n = 1, 2, 3, ...
The sum of the first k terms of this sequence is 12k - 3*k*(k+1)/2
Therefore 12k - 3k*(k+1)/2 = 0
12k = 3k*(k+1)/2
8 = k+1
so that k = 7
Wiki User
∙ 11y ago
To solve this arithmetic series problem, you can use the formula: Sn = (n/2) * (2a + (n-1)d), where Sn is the sum of the series, a is the first term, d is the common difference, and n is the number of terms. Substituting the given values, we have: 0 = (n/2) * (2(9) + (n-1)(-3)). Simplifying, we get: 0 = (n/2) * (18 - 3n + 3). Rearranging and simplifying further, we have: 0 = 9n^2 - 27n. Factoring out n, we get: n(9n - 27) = 0. Therefore, either n = 0 or n = 3. Since the number of terms cannot be zero, the number of terms in the series is 3.
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From the information given, all that can be said is that it will be a negative number.
What is a sequence whose successive terms differ by the same nonzero number d called the common difference?
It's technically called an arithmetic sequence
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A single number, such as 11111, cannot define an arithmetic sequence. On the other hand, it can be the first element of any kind of sequence. On the other hand, if the question was about ``1, 1, 1, 1, 1'' then that is an arithmetic sequence as there is a common difference of 0 between each term.
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The quotient is the answer in a division problem.
What is the difference from a math problem?
The difference is nthe number answer after subtracting.
What is the common difference?
The difference between each number in an arithmetic series
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could also be negative
What is the common difference used to make an arithmetic sequence where the first number is 14 and the 16th number is 104?
6
What is the common difference for an arithmetic sequence in which the terms are decreasing?
From the information given, all that can be said is that it will be a negative number.
What is the difference between number theory and arithmetic?
arithmetic starts with m while number theory starts with n
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The numbers are in an arithmetic sequence (common difference = 6). Since there are 5 of them, their mean is the middle number: 79.
How can you get the common difference in an arithmetic sequence?
You subtract any two adjacent numbers in the sequence. For example, in the sequence (1, 4, 7, 10, ...), you can subtract 4 - 1, or 7 - 4, or 10 - 7; in any case you will get 3, which is the common difference.
What is a sequence whose successive terms differ by the same nonzero number d called the common difference?
It's technically called an arithmetic sequence
What is it called when a problem only has number?
Problems that have only numbers are problems in arithmetic.
Why is 11111 an arithmetic sequence?
A single number, such as 11111, cannot define an arithmetic sequence. On the other hand, it can be the first element of any kind of sequence. On the other hand, if the question was about ``1, 1, 1, 1, 1'' then that is an arithmetic sequence as there is a common difference of 0 between each term.
What is meaning of Quotient?
The quotient is the answer in a division problem.
In a math problem what is the difference of a number?
It is the answer to a subtraction problem.
