NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 5: Arithematic Progressions - Exercise 5.1Question 10
Class 10 - Mathematics - CHAPTER 5: Arithematic Progressions - Exercise 5.1
Question. 10
What is the common difference of an AP in which \(a_{18}-a_{14}=32\)?
(A)
8
(B)
−8
(C)
−4
(D)
4
Detailed Answer with Explanation:
We are given: \(a_{18} - a_{14} = 32\).
Step 1: Recall the formula for the \(n^{th}\) term of an AP: \(a_n = a + (n-1)d\), where \(a\) is the first term and \(d\) is the common difference.
Step 2: The difference between two terms in an AP depends only on the difference of their positions: \(a_m - a_n = (m - n)d\).
Step 3: Here, \(m = 18\) and \(n = 14\). So, \(a_{18} - a_{14} = (18 - 14)d = 4d\).
Step 4: We are told this difference is 32. So, \(4d = 32\).
Step 5: Divide both sides by 4: \(d = \dfrac{32}{4} = 8\).
Therefore, the common difference is 8.