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How many terms of the a.p 24,21,18....must be taken so that the sum is 78?Give reason for your double answer

Posted by Ehatesham Ansari 6 years, 2 months ago

CBSE > Class 10 > Mathematics

1 answers

Yogita Ingle 6 years, 2 months ago

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

{tex} 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{/tex}

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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