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Question
How many terms of the A.P. : 24, 21, 18, ................ must be taken so that their sum is 78?
Solution
Let the number of terms taken be n.
The given A.P. is 24, 21, 18, ................
Here, a = 24 and d = 21 – 24 = –3
`S = n/2 [2a + (n - 1)d]`
`=> 78 = n/2 [2 xx 24 + (n - 1)xx (-3)]`
`=> 78 = n/2 [48 - 3n + 3]`
`=>` 156 = n[51 – 3n]
`=>` 156 = 51n – 3n2
`=>` 3n2 – 51n + 156 = 0
`=>` n2 – 17n + 52 = 0
`=>` n2 – 13n – 4n + 52 = 0
`=>` n(n – 13) – 4(n – 13) = 0
`=>` (n – 13)(n – 4) = 0
`=>` n = 13 or n = 4
∴ Required number of terms = 4 or 13
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