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Q: 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.?

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An arithmetic series is the sum of the terms in an arithmetic progression.

It is 58465.

The sequence is arithmetic if the difference between every two consecutive terms is always the same.

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.

a1=2 d=3 an=a1+(n-1)d i.e. 2,5,8,11,14,17....

RAMANUJANRAMANUJAN

49

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

-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.

The arithmetic mean is an average arrived at by adding all the terms together and then dividing by the number of terms.

The arithmetic mean.

An arithmetic sequence.

An arithmetic-geometric mean is a mean of two numbers which is the common limit of a pair of sequences, whose terms are defined by taking the arithmetic and geometric means of the previous pair of terms.

The question cannot be answered because two terms are not enough to determine whether the sequence is arithmetic or geometric (or something else).

29

No, the Fibonacci sequence is not an arithmetic because the difference between consecutive terms is not constant

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.

Adding together the terms and dividing them by the number of terms gives the arithmetic mean.

The mean, or the average.

For an Arithmetic Progression, Sum = 15[a + 7d].{a = first term and d = common difference} For a Geometric Progression, Sum = a[1-r^15]/(r-1).{r = common ratio }.

In engineering terms, Ra is the arithmetic meaning for roughness of a surface, and is also referred to as arithmetic average.

The nth term of an arithmetic sequence = a + [(n - 1) X d]

arithmetic sequence

AP - Arithmetic ProgressionGP - Geometric ProgressionAP:An AP series is an arithmetic progression, a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 3, 5, 7, 9, 11, 13, … is an arithmetic progression with common difference 2. If the initial term of an arithmetic progression is and the common difference of successive members is d, then the nth term of the sequence is given by:and in generalA finite portion of an arithmetic progression is called a finite arithmetic progression and sometimes just called an arithmetic progression.The behavior of the arithmetic progression depends on the common difference d. If the common difference is:Positive, the members (terms) will grow towards positive infinity.Negative, the members (terms) will grow towards negative infinity.The sum of the members of a finite arithmetic progression is called an arithmetic series.Expressing the arithmetic series in two different ways:Adding both sides of the two equations, all terms involving d cancel:Dividing both sides by 2 produces a common form of the equation:An alternate form results from re-inserting the substitution: :In 499 AD Aryabhata, a prominent mathematician-astronomer from the classical age of Indian mathematics and Indian astronomy, gave this method in the Aryabhatiya (section 2.18) .[1]So, for example, the sum of the terms of the arithmetic progression given by an = 3 + (n-1)(5) up to the 50th term isGP:A GP is a geometric progression, with a constant ratio between successive terms. For example, the series is geometric, because each successive term can be obtained by multiplying the previous term by 1 / 2.Geometric series are one of the simplest examples of infinite series with finite sums, although not all of them have this property. Historically, geometric series played an important role in the early development of calculus, and they continue to be central in the study of convergence of series. Geometric series are used throughout mathematics, and they have important applications in physics, engineering, biology, economics, computer science, queuing theory, and finance.

The series appears to be an arithmetic series in which the n'th term is 1.5 + (n - 1)2.5. If so, the next two terms are 11.5 and 14.