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How many terms of the AP : 24, 21,18,......

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

Text Solution

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a=24 and d=21-24=-3
`S_n=n/2(2a+(n-1)d)`
`78=n/2(2(24)+(n-1)(-3))`
156=n(48-3n+3)
`n^2-51n+156=0`
n(n-13)-4(n-13)=0
(n-4)(n-13)
n=4,13
...
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