Properties of Common Difference
- In an AP, the common difference remains constant throughout the sequence. This means that the difference between any two consecutive terms is always the same.
- When we multiply an AP with a constant term (say k ) then the new common difference will be k times the previous common difference.
- When two AP are added / subtracted then the common difference of the resulting AP Will be the sum / difference of the common difference of given two AP
- When two AP are Multiplied / divided then the common difference of the resulting AP Will be the multiplication / quotient of the common difference of given two AP .
- A positive value of common difference shows the AP is increasing AP.
- A negative value of common difference shows the AP is decreasing AP.
- A null value of common difference (or 0) shows the AP is constant AP.
Note that here addition operation refers to adding the 1st , 2nd , 3rd . . . . nth term of first AP in the 1st , 2nd , 3rd . . . . nth term of the second AP and same goes for subtraction, multiplication, division.
What is the common difference of the AP 1/b, (3-b)/3b, (3-2b)/3b…?
Common difference of the given AP (1/b , (3-b) / 3b , (3-2b) / 3b … ) is -1/3 and can be calculated using the general formulas for finding the common difference of an AP . In this article, we are going to learn about the concept of common differences, explore methods to determine them , and apply our knowledge to solve similar problems efficiently.
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