Question

Find the common difference of the following A.P:
                  1, 4, 7, 10, 13, 16,.....

Answer 1

Hint: First of all we have to know about the arithmetic progression (A.P). It is a sequence of numbers such that the difference of the consecutive terms is constant. Difference here means the second minus the first. The difference between any two consecutive terms of an A.P is always a constant. This constant is equal to the common difference of the A.P.

Complete step-by-step solution -
We have been given the A.P as following:
1, 4, 7, 10, 13, 16.....
Here, the difference between any two consecutive terms are as shown belows:
$(4-1)=(7-4)=(10-7)=(13-10)=(16-13)=3$
So, this difference is constant which is equal to the common difference of the given A.P.
Therefore, the common difference of the A.P is equal to 3.

Note: Just remember that the difference between the successive and the preceding term of an A.P is always constant and this is equal to the common difference of an A.P.
The common difference of an A.P can be positive or negative. If the common difference is positive then the terms will grow towards positive infinity and if the common difference is negative then the terms will grow towards negative infinity.