NCERT Class X Chapter 5: Arithmetic Progression Example 15

Question:

Find the sum of first 24 terms of the list of numbers whose nth term is given by a_n = 3 + 2n

Given:

The nth term of the list of numbers is given by a_n = 3 + 2n. We need to find the sum of the first 24 terms.

To Find:

The sum of the first 24 terms (S₂₄).

Formula:

The sum of an arithmetic series is given by: S_n = n 2 (a₁ + a_n), where n is the number of terms, a₁ is the first term, and a_n is the last term.

Solution:

First, let's find the first term (a₁) and the 24^th term (a₂₄).

a₁ = 3 + 2(1) = 5

a₂₄ = 3 + 2(24) = 51

Now, we can use the formula for the sum of an arithmetic series:

S₂₄ = 24 2 (a₁ + a₂₄) ⇒ S₂₄ = 12(5 + 51) ⇒ S₂₄ = 12(56) = 672

Result:

The sum of the first 24 terms is 672.

Next question solution:

NCERT Class X Chapter 5: Arithmetic Progression Example 16(i)

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