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The sum of the first 5 terms of an arithmetic series is 85. The sum of the first 6 terms is 123. Determine the first four terms of the series.?
Wiki User
∙ 14y ago
Suppose the first term is a, the second is a+r and the nth is a+(n-1)r.
Then the sum of the first five = 5a + 10r = 85
and the sum of the first six = 6a + 15r = 123
Solving these simultaneous equations, a = 3 and r = 7
So the first four terms are: 3, 10, 17 and 24
Wiki User
∙ 14y ago
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What is an arithmetic series?
An arithmetic series is the sum of the terms in an arithmetic progression.
New series is created by adding corresponding terms of an arithmetic and geometric series If the third and sixth terms of the arithmetic and geometric series are 26 and 702 find for the new series S10?
It is 58465.
What are the answers for Arithmetic and Geometric Sequences gizmo?
Arithmetic : (First term)(last term)(act of terms)/2 Geometric : (first term)(total terms)+common ratio to the power of (1+2+...+(total terms-1))
The sum of the first 5 terms of an arithmetic sequence is 40 and the sum of its first ten terms is 155what is this arithmetic sequence?
a1=2 d=3 an=a1+(n-1)d i.e. 2,5,8,11,14,17....
What is the sum of all the numbers from 51 to 150?
This is an arithmetic series, so we use the formula S=n/2 (a+l) when n is the number of terms, a is the first number and l the last. S = 100/2 (51 + 150) =50 (201) = 10050
What is an arithmetic series?
An arithmetic series is the sum of the terms in an arithmetic progression.
New series is created by adding corresponding terms of an arithmetic and geometric series If the third and sixth terms of the arithmetic and geometric series are 26 and 702 find for the new series S10?
It is 58465.
What is the difference between an arithmetic series and a geometric series?
An arithmetic series is the sequence of partial sums of an arithmetic sequence. That is, if A = {a, a+d, a+2d, ..., a+(n-1)d, ... } then the terms of the arithmetic series, S(n), are the sums of the first n terms and S(n) = n/2*[2a + (n-1)d]. Arithmetic series can never converge.A geometric series is the sequence of partial sums of a geometric sequence. That is, if G = {a, ar, ar^2, ..., ar^(n-1), ... } then the terms of the geometric series, T(n), are the sums of the first n terms and T(n) = a*(1 - r^n)/(1 - r). If |r| < 1 then T(n) tends to 1/(1 - r) as n tends to infinity.
How do you determine if a sequence is arithmetic?
The sequence is arithmetic if the difference between every two consecutive terms is always the same.
What are the answers for Arithmetic and Geometric Sequences gizmo?
Arithmetic : (First term)(last term)(act of terms)/2 Geometric : (first term)(total terms)+common ratio to the power of (1+2+...+(total terms-1))
The sum of the first 5 terms of an arithmetic sequence is 40 and the sum of its first ten terms is 155what is this arithmetic sequence?
a1=2 d=3 an=a1+(n-1)d i.e. 2,5,8,11,14,17....
The answer to this question Find the sum of the first 25 elements what series -5 19 43 67?
-5 19 43 67 ...This is an arithmetic sequence because each term differs from the preceding term by a common difference, 24.In order to find the sum of the first 25 terms of the series constructed from the given arithmetic sequence, we need to use the formulaSn = [2t1 + (n - 1)d] (substitute -5 for t1, 25 for n, and 24 for d)S25 = [2(-5) + (25 - 1)24]S25 = -10 + 242S25 = 566Thus, the sum of the first 25 terms of an arithmetic series is 566.
What is the sum of all the numbers from 51 to 150?
This is an arithmetic series, so we use the formula S=n/2 (a+l) when n is the number of terms, a is the first number and l the last. S = 100/2 (51 + 150) =50 (201) = 10050
Who gave the formula for finding sum of the first 'n' terms in Arithmetic Progression?
RAMANUJANRAMANUJAN
What is the sum of the first ten terms of the arithmetic sequence 4 4.2 4.4...?
49
What formula represents the partial sum of the first n terms of the series 5 10 15 20 25?
The series given is an arithmetic progression consisting of 5 terms with a common difference of 5 and first term 5 → sum{n} = (n/2)(2×5 + (n - 1)×5) = n(5n + 5)/2 = 5n(n + 1)/2 As no terms have been given beyond the 5th term, and the series is not stated to be an arithmetic progression, the above formula only holds for n = 1, 2, ..., 5.
What is the definition of an arithmetic mean?
The arithmetic mean is an average arrived at by adding all the terms together and then dividing by the number of terms.
