NCERT Class X Chapter 5: Arithmetic Progression Example 11

Question:

Find the sum of the first 22 terms of the AP : 8, 3, –2, . . .

Given:

An Arithmetic Progression (AP) with first term a = 8, common difference d = 3 - 8 = -5, and number of terms n = 22.

To Find:

The sum of the first 22 terms of the AP, denoted by S₂₂.

Formula:

The sum of the first n terms of an AP is given by the formula: S_n = n2(2a + (n - 1)d)

Solution:

Given a = 8, d = -5, and n = 22.

Substituting these values into the formula for S_n:

S₂₂ = 222(2(8) + (22 - 1)(-5))

⇒ S₂₂ = 11(16 + 21(-5))

⇒ S₂₂ = 11(16 - 105)

⇒ S₂₂ = 11(-89)

⇒ S₂₂ = -770

Result:

Therefore, the sum of the first 22 terms of the AP is -770.

Next question solution:

NCERT Class X Chapter 5: Arithmetic Progression Example 12

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