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How many terms of the A.P. 17+15+13+… has the sum 72? Explain the double answer.

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The correct Answer is:N/a

Here a=17, d=15-17=-2
Let Sn=72
⇒ n2[2a+(n−1)d]=72
⇒ n2[2×17+(n−1)(−2)]=72
⇒ n2[34+(n−1)(−2)]=72
⇒ n2(34−2n+2)=72
⇒ n(18−n)=72
⇒ n2−18n+72=0
⇒ (n−6)(n−12)=0
⇒ n−6=0orn−12=0
⇒ n=6orn=12.
The sum of next 6 terms after first 6 terms is zero, so the sum of first 6 terms is equal to the sum of first 12 terms.

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