NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 5: Arithematic Progressions - Exercise 5.1Question 1
Class 10 - Mathematics - CHAPTER 5: Arithematic Progressions - Exercise 5.1
Question. 1
In an AP, if \(d=-4\), \(n=7\), \(a_n=4\), then \(a\) is
(A)
6
(B)
7
(C)
20
(D)
28
Detailed Answer with Explanation:
We are asked to find the first term \(a\) of the Arithmetic Progression (AP).
Step 1: Recall the formula for the \(n^{th}\) term of an AP:
\(a_n = a + (n - 1) d\)
Step 2: Substitute the given values: \(a_n = 4\), \(n = 7\), \(d = -4\).
So, \(4 = a + (7 - 1)(-4)\).
Step 3: Simplify inside the brackets:
\(7 - 1 = 6\). So,
\(4 = a + (6)(-4)\).
Step 4: Multiply:
\(4 = a - 24\).
Step 5: Add 24 on both sides to find \(a\):
\(a = 4 + 24\).
Step 6: Calculate:
\(a = 28\).
So, the first term \(a\) is 28.