Find the number of the terms of the AP : 36,32,28.. which must be taken so that the sum is 180 . Explain the double answer.
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Answer:
180=n/2(2a+(n-1)d
180=n/2(2(36)+(n-1)
180=n/2(72+(n-1)-4
180=n/2(72-4n+4)
180=n/2(-4n+76)
180×2=n(-4n+76)
360=-4n2+76n
4n2-76n+360=0
4(n2-19n+90)=0
n2-19n+90=0
n(n-9)-10(n-9)=0
n=9, n=10
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