Mathematics · Arithmetic Progressions · NCERT Examples

Example 11

A complete, independently verified solution for NCERT Example 11.

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Mathematics · Chapter 5 · NCERT Examples

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NCERT Example

sum of AP

Find the sum of the first 22 terms of 8,3,−2,…

Board-exam working:

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

Here a=8,d=3−8=−5,n=22.

S₂₂=22/2[2×8+(22−1)(−5)]=11[16−105]=11(−89)=−979.

The last term is a₂₂=8+21(−5)=−97, and 22/2(8−97)=11(−89)=−979, confirming the sum.

−979.