Mathematics · Arithmetic Progressions · NCERT Examples
Example 13
A complete, independently verified solution for NCERT Example 13.
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Mathematics · Chapter 5 · NCERT Examples
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NCERT Example
Example 13
How many terms of 24,21,18,… must be taken so their sum is 78?
Solution
Board-exam working:
Here a=24,d=−3,Sₙ=78.
78=n/2[2×24+(n−1)(−3)]=n/2[48−3n+3]=n/2(51−3n).
Therefore 156=51n−3n², so 3n²−51n+156=0.
Dividing by 3 gives n²−17n+52=0=(n−4)(n−13).
Hence n=4 or n=13.
Check: S₄=4/2[48−9]=2×39=78, and S₁₃=13/2[48−36]=13/2×12=78.
Final answer
4 terms or 13 terms.