NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 5: Arithematic Progressions - Exercise 5.1Question 11
Class 10 - Mathematics - CHAPTER 5: Arithematic Progressions - Exercise 5.1
Question. 11
Two APs have the same common difference. The first term of one is \(-1\) and of the other is \(8\). Then the difference between their 4th terms is
(A)
−1
(B)
−8
(C)
7
(D)
−9
Detailed Answer with Explanation:
Step 1: The formula for the \(n^{th}\) term of an AP is:
\(a_n = a + (n-1) \times d\)
Step 2: For the first AP, the first term \(a = -1\) and the common difference is \(d\).
So, the 4th term = \(-1 + (4-1) \times d = -1 + 3d\).
Step 3: For the second AP, the first term \(a = 8\) and the common difference is the same \(d\).
So, the 4th term = \(8 + (4-1) \times d = 8 + 3d\).
Step 4: Now, find the difference between the 4th terms:
\((-1 + 3d) - (8 + 3d) = -1 + 3d - 8 - 3d = -9\).
Step 5: Therefore, the difference between their 4th terms is \(-9\).