Mathematics · Arithmetic Progressions · NCERT Examples

Example 15

A complete, independently verified solution for NCERT Example 15.

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Mathematics · Chapter 5 · NCERT Examples

Verified NCERT questions and solutionsSolutions are checked independently and follow the supplied NCERT chapter edition.

NCERT Example

sum of AP

Find the sum of the first 24 terms when aₙ=3+2n.

Board-exam working:

S_n=\frac{n}{2}[2a+(n-1)d]=\frac{n}{2}(a+l)

Put n=1,2,3: a₁=3+2=5,a₂=3+4=7,a₃=3+6=9.

Thus a=5 and d=2.

S₂₄=24/2[2×5+(24−1)2]=12[10+46]=12×56=672.

Check using the last term: a₂₄=3+2×24=51, so S₂₄=24/2(5+51)=12×56=672.

672.