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Can zero be common difference for arithmetic progression?
Yes but the progression would be a degenerate one.
What is the difference between arithmetic progression and geometric progression?
In an arithmetic progression the difference between each term (except the first) and the one before is a constant. In a geometric progression, their ratio is a constant. That is, Arithmetic progression U(n) - U(n-1) = d, where d, the common difference, is a constant and n = 2, 3, 4, ... Equivalently, U(n) = U(n-1) + d = U(1) + (n-1)*d Geometric progression U(n) / U(n-1) = r, where r, the common ratio is a non-zero constant and n = 2, 3, 4, ... Equivalently, U(n) = U(n-1)*r = U(1)*r^(n-1).
How can a sequence be both arithmetic and geometric?
A sequence can be both arithmetic and geometric if it consists of constant values. For example, the sequence where every term is the same number (e.g., 2, 2, 2, 2) is arithmetic because the difference between consecutive terms is zero, and it is geometric because the ratio of consecutive terms is also one. In such cases, the sequence meets the criteria for both types, as both the common difference and the common ratio are consistent.
What is the common ratio of the geometric progression?
The common ratio is the ratio of the nth term (n > 1) to the (n-1)th term. For the progression to be geometric, this ratio must be a non-zero constant.
Differentiate between arithmetic series and geometric series?
In an arithmetic series, each term is defined by a fixed value added to the previous term. This fixed value (common difference) may be positive or negative.In a geometric series, each term is defined as a fixed multiple of the previous term. This fixed value (common ratio) may be positive or negative.The common difference or common ratio can, technically, be zero but they result in pointless series.
Can zero be common difference for arithmetic progression?
Yes but the progression would be a degenerate one.
What is the difference between arithmetic progression and geometric progression?
In an arithmetic progression the difference between each term (except the first) and the one before is a constant. In a geometric progression, their ratio is a constant. That is, Arithmetic progression U(n) - U(n-1) = d, where d, the common difference, is a constant and n = 2, 3, 4, ... Equivalently, U(n) = U(n-1) + d = U(1) + (n-1)*d Geometric progression U(n) / U(n-1) = r, where r, the common ratio is a non-zero constant and n = 2, 3, 4, ... Equivalently, U(n) = U(n-1)*r = U(1)*r^(n-1).
What is the difference of arithmetic progression to geometric progression?
In an arithmetic progression the difference between each term (except the first) and the one before is a constant. In a geometric progression, their ratio is a constant.That is,Arithmetic progressionU(n) - U(n-1) = d, where d, the common difference, is a constant and n = 2, 3, 4, ...Equivalently,U(n) = U(n-1) + d = U(1) + (n-1)*dGeometric progressionU(n) / U(n-1) = r, where r, the common ratio is a non-zero constant and n = 2, 3, 4, ...Equivalently,U(n) = U(n-1)*r = U(1)*r^(n-1).
How can a sequence be both arithmetic and geometric?
A sequence can be both arithmetic and geometric if it consists of constant values. For example, the sequence where every term is the same number (e.g., 2, 2, 2, 2) is arithmetic because the difference between consecutive terms is zero, and it is geometric because the ratio of consecutive terms is also one. In such cases, the sequence meets the criteria for both types, as both the common difference and the common ratio are consistent.
What is the common ratio of the geometric progression?
The common ratio is the ratio of the nth term (n > 1) to the (n-1)th term. For the progression to be geometric, this ratio must be a non-zero constant.
Differentiate between arithmetic series and geometric series?
In an arithmetic series, each term is defined by a fixed value added to the previous term. This fixed value (common difference) may be positive or negative.In a geometric series, each term is defined as a fixed multiple of the previous term. This fixed value (common ratio) may be positive or negative.The common difference or common ratio can, technically, be zero but they result in pointless series.
In an arithmetic sequence the constant rate of increase or decrease between successive terms is called the?
In an arithmetic sequence, the constant rate of increase or decrease between successive terms is called the common difference. This value can be positive, negative, or zero, depending on whether the sequence is increasing, decreasing, or constant. The common difference is denoted by the symbol ( d ) and is calculated by subtracting any term from the subsequent term.
Can you divide a fraction by zero?
Division by zero is not possible in arithmetic.
Is 1 1 1 1 1 an arithmetic sequence?
Yes, with a difference of zero between terms. It is also a geometric series, with a ratio of 1 in each case.
What is the difference between a geometric sequence and arithmetic sequence?
Goemetric sequence : A sequence is a goemetric sequence if an/an-1is the same non-zero number for all natural numbers greater than 1. Arithmetic sequence : A sequence {an} is an arithmetic sequence if an-an-1 is the same number for all natural numbers greater than 1.
What is the significance of two's complement zero in binary arithmetic?
In binary arithmetic, two's complement zero is significant because it represents the neutral or "zero" value in the system. It serves as a reference point for positive and negative numbers, allowing for efficient addition and subtraction operations.
Number Progression 10 9 7 4?
The next term is 'zero'.
