Common Difference

Question 1. What is the common difference of an A.P.?

Solution:

The common difference of an A.P. is defined as the difference between the next and previous terms and its preceding term. Its value is always a fixed constant and same for entire progression.

Question 2. Write the formula for calculating the sum of an arithmetic progression in terms of common difference.

Solution:

The sum of an A.P. is given by the formula:

S = n/2 [2a + (n – 1)d]

where,

• S is the sum of the series
• n is the number of terms
• a is the first term
• d is the common difference

Question 3. How does the common difference change when all the terms of an A.P. are increased by a value of 5?

Solution:

The common difference increases on increases in the value of terms and decreases on decreases in the value of terms. So, it will also increase by a value of 5.

Arithmetic has most likely the longest history at the time. It is a method of computation that has been used since ancient times to derive definite values for routine calculations such as measurements, labelling, and other day-to-day calculations. The phrase derives from the Greek word “arithmos,” which translates as “numbers.”

Arithmetic is the basic branch of mathematics that studies numbers and the characteristics of classical operations such as addition, subtraction, multiplication, and division.

Besides the basic operations of addition, subtraction, multiplication, and division, arithmetic also includes advanced computations such as percentage, logarithm, exponentiation, and square roots, among others. Arithmetic is the study of numerals and their traditional operations.