Similar Problems
Problem 1: Calculate the common difference of the AP 156, 131, 106, 81, 56.
Solution:
Common difference can be calculated as
d = 131-156
d = 25
Hence, the common difference of the AP is 25.
Problem 2: If the 10th term of an AP is 50 and the 15th term is 65, find the common difference of the AP.
Solution:
Given
10th term = a + 9d = 50
15th term = a + 14d = 65
subtracting both terms
(a + 14d ) – ( a+9d ) = 65 – 50
5d = 15
d = 3
Hence, the common difference of the AP is 3.
Problem 3: Find the common difference of the AP, 99, 88, 77, 66…
Solution:
Common difference can be calculated as
d = 88 – 99
d = -11
Hence, the common difference of the AP is -11.
Problem 4 : The first term of an AP is 3 and the last term is 31. If there are 15 terms in the AP, find the common difference.
Solution:
Given a =3
an=a + (n-1 )d = 31 , where n = 15
= 3 + (15-1 ) d = 31
=> 14d = 28
=> d = 2
Hence the common difference of the given AP is 2
Problem 5 : Find the common difference of the AP : log2 , log4 , log8 , log16 , log32 …… .
Solution:
From the Given Sequence
a = log2
a + d = log4
So, (a+d ) – a = log4 – log2
d = log4/2 = log2
Hence the common difference of the AP is log2
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.