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What is the common difference of the AP 1/b, (3-b)/3b, (3-2b)/3b…?

  • Last Updated : 01 Sep, 2021

A sequence is defined as the list of numbers that are arranged in a sequential manner. A series is defined as an arrangement of a set of numbers in a particular order that follows some rule. Let us say that m1, m2, m3, m4,… etc. denote the terms of a sequence, then the numbers 1, 2, 3, 4,… denote the position of the terms of the sequence. There are several types of sequences. Some of them are,

  • Arithmetic Sequences
  • Geometric Sequences
  • Harmonic Sequences

An arithmetic sequence is a sequence in which every next term is obtained by the addition or subtraction of a given number to the preceding number. A geometric sequence is a sequence in which every next term is obtained by dividing or multiplying by a given number to the preceding number. A harmonic sequence is a sequence in which the reciprocal of all the terms form an arithmetic sequence.

Arithmetic Sequence

An arithmetic progression (AP) is a sequence whose each term is obtained by adding or subtracting a fixed number to the previous term. Arithmetic sequences can be both Increasing or decreasing in nature. The fixed number that is added or subtracted to the previous term is known as a common difference. Hence, the common difference can be calculated by subtracting a term of the arithmetic sequence by its preceding term.

 Calculate the common difference of the AP 1/b, (3-b)/3b, (3-2b)/3b

As mentioned above, the common difference is the term which is the difference between two consecutive terms in an AP, the common difference is fixed for an AP and is denoted as “d”. To solve the problem statement mentioned above, let’s see the steps involved to find the common difference,

Steps to calculate the common difference

  • Take any term of the given sequence except the first term.
  • Subtract the term with its preceding term.
  • Make sure the calculation is correct.
  • Check the same for any other term of the sequence.

The difference of the numbers is the common difference,

For example: 

Let us calculate the common difference of the a arithmetic sequence 1, 3, 5, 7, 9. 

Given that the sequence is 1, 3, 5, 7, 9.

The common difference can be calculated as

d = 3-1 = 5-3 = 7-5 = 9-7

d = 2

Hence, the common difference of the given sequence is 2.

What is the common difference of the AP 1/b, (3-b)/3b, (3-2b)/3b…?

As explained above, let’s solve the AP mentioned in the problem statement:

Given that the arithmetic progression is 1/b, (3-b)/3b. (3-2b)/3b.

The common difference can be calculate as,

d = (3-b)/3b-1/b

d = (3-b-3)/3b

d = -b/3b

d = -1/3

Hence, the common difference of the AP is -1/3

Similar Problems

Question 1: Calculate the common difference of the AP 156, 131, 106,  81, 56.

Solution:

The common difference can be calculated as

d = 131-156

d = 25

Hence, the common difference of the AP is 25.

Question 2: Calculate the common difference of the AP 324, 397, 470, 543, 616.

Solution:

The common difference can be calculated as

d = 397-324

d = 73

Hence, the common difference of the AP is 73.

Question 3: Find the common difference of the AP, 99, 88, 77, 66…

Solution:

The common difference can be calculated as

d = 88 – 99

d = -11

Hence, the common difference of the AP is -11.

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