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Q: Can zero be the common difference for arithmetic progression?

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Yes but the progression would be a degenerate one.

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).

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).

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.

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.

Division by zero is not possible in arithmetic.

Yes, with a difference of zero between terms. It is also a geometric series, with a ratio of 1 in each case.

The only arithmetic exception I can think of seeing has been caused by a division by zero statement. Trying to do integer division by 0 or mod 0 will result in this arithmetic exception. Note that floating point division by zero will result in "Infinity" being returned, and floating point modulus will result in "NaN" being returned.

The next term is 'zero'.

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.

There is no symbol for zero, which makes it very difficult to do arithmetic.

It contained a zero symbol which made arithmetic a lot easier.

ArithmeticException, as the name implies denotes a general arithmetic error such as diving by zero.

Any arithmetic operation, other than division by zero, can be performed on any set of numbers in a sequence.

One divided by zero is an undefined operation, which leads to contradictions and nonsense.For this reason, division by zero is forbidden in arithmetic.

Because Hindu-Arabic numerals contains a zero symbol which makes arithmetic a lot easier to calculate whereas Roman numerals have no zero symbol thus making arithmetic more difficult to calculate.

Their DIFFERENCE will be zero if and only if they have the SAME direction.

which type of bond is formed when there is zero difference in electronegativity

Zero. In general, the difference between any number and itself is zero.

Zero was not discovered because it was conceived by ancient mathematicians thus making arithmetic easier for positional place value purposes as for example 23 is different to 203.

A Neutral, Common, or Ground.

Coke zero is the same as sprite zero

If you subtract zero from 67 the difference will be 67 so it is true.

The Romans did not have the concept of zero-- there is no Roman numeral for zero. This lack made it virtually impossible to do arithmetic with Roman numerals and that is why we use Arabic numerals nowadays.

A fraction such that the divisor (denominator) is zero is undefined. Such a division is expressed as x/0 where x is the dividend (numerator). In ordinary arithmetic, the expression has no meaning so division by zero is undefined.