Mathematics · Chapter 5 · NCERT Examples
Verified NCERT questions and solutionsSolutions are checked independently and follow the supplied NCERT chapter edition.
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.