NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.3 Question3(ix)

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.3 Question 3 (ix)

Question

In an AP: given a = 3, n = 8, S = 192, find d.

Given

a = 3, n = 8, S = 192

To Find

Common difference (d)

Formula

Sum of an arithmetic progression = Sn = n 2 [2a + (n - 1)d]

Solution

Substitute the given values into the formula: Sn = n2(2a + (n - 1)d), we have:

192 = 8 2 [2(3) + (8 - 1)d]

Simplify the equation:

192 = 4[6 + 7d]

Divide both sides by 4:

48 = 6 + 7d

Subtract 6 from both sides:

42 = 7d

Divide both sides by 7:

d = 6

Result

The common difference (d) is 6.

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