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Find the sum of an arithmetic progression of seventeen terms whose middle term is 5?
Wiki User
∙ 14y ago
85 (=17*5).
The middle term is 5. There are 8 terms bigger than 5 and 8 smaller.
The term smaller than 5 and next to it is 5 - r
The term bigger than 5 and next to it is 5 + r
So these two average 5.
Similarly, the next pair outwards average 5; and so on.
So the sum of the progression is equivalent to the sum of 8 pairs of numbers whose average is 5 and the middle term which is 5 ie 17 lots of 5.
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.
Who gave the formula for finding sum of the first 'n' terms in Arithmetic Progression?
RAMANUJANRAMANUJAN
The 7th term of an arithmetic progression is 6 The sum of the first 10 terms is 30 Find the 5th term of the progression?
2
What is the sum of the first 15 terms of an arithmetic?
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 }.
Is -2-6-18-54-162-468-1458 geometric or arithmetic?
It is neither. (-6) - (-2) = -4 (-18) - (-6) = -12 which is not the same as -4. Therefore it is not an arithmetic progression - which requires the difference between successive terms to be the same. Also -162/-54 = 3 -468/-162 = 2.88... recurring, and that is not the same as 3. Therefore it is not a geometric progression - which requires the ratio of terms to be the same.
What is an arithmetic series?
An arithmetic series is the sum of the terms in an arithmetic progression.
What is harmonic sequence?
It is a progression of terms whose reciprocals form an arithmetic progression.
Arithmetic progression?
This a progression that involves addition or subtraction of successive terms in a sequence.
Who gave the formula for finding sum of the first 'n' terms in Arithmetic Progression?
RAMANUJANRAMANUJAN
The 7th term of an arithmetic progression is 6 The sum of the first 10 terms is 30 Find the 5th term of the progression?
2
8th termof an arithematic progression is16 what is its 12th term?
Any number you like. You need two terms to uniquely identify an arithmetic progression.
What is the sum of the first 15 terms of an arithmetic?
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 }.
Formula to find out the sum of n terms?
It is not possible to answer this question without information on whether the terms are of an arithmetic or geometric (or other) progression, and what the starting term is.
What is the sum of fifteen terms of arithmetic progresion whose eighth term is 4?
This question is impossible to answer without knowing the difference between successive terms of the progression.
Find the sum of an A.P of seventeen terms whose middle term is 5?
It is 85.
Difference between AP series GPs reis?
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.
Is -2-6-18-54-162-468-1458 geometric or arithmetic?
It is neither. (-6) - (-2) = -4 (-18) - (-6) = -12 which is not the same as -4. Therefore it is not an arithmetic progression - which requires the difference between successive terms to be the same. Also -162/-54 = 3 -468/-162 = 2.88... recurring, and that is not the same as 3. Therefore it is not a geometric progression - which requires the ratio of terms to be the same.
