How many terms of ap 24 21 18


Asked by admin @ in Math viewed by 303 People


How many terms of the AP : 24, 21, 18, . . . must be taken so that their sum is 78?

Answered by admin @



First term, a = 24
common difference, d = 21-24 = -3
let the number of terms to get sum 78 is n.

 S_n=78\\ \\ \Rightarrow \frac{n}{2}(2a+(n-1)d)=78\\ \\  \Rightarrow \frac{n}{2}(2 \times 24+(n-1)(-3))=78\\ \\  \Rightarrow n(48-3n+3)=78 \times 2\\ \\ \Rightarrow -3n^2+51n-156=0\\ \\ \Rightarrow 3n^2-51n+156=0

Solving the quadratic equation, we get n=4 and n=13.
So you can take either 4 terms or 13 terms to get the sum 78.

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