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प्रश्न
How many terms of the series 18 + 15 + 12 + ........ when added together will give 45?
उत्तर
Here, we find that
15 – 18 = 12 – 15 = –3
Thus, the given series is an A.P. with first term 18 and common difference –3.
Let the number of terms to be added be 'n'.
`S_n = n/2 [2a + (n - 1)d]`
`\implies 45 = n/2 [2(18) + (n - 1)(-3)]`
`\implies` 90 = n[36 – 3n + 3]
`\implies` 90 = n[39 – 3n]
`\implies` 90 = 3n[13 – n]
`\implies` 30 = 13n – n2
`\implies` n2 – 13n + 30 = 0
`\implies` n2 – 10n – 3n + 30 = 0
`\implies` n(n – 10) – 3(n – 10) = 0
`\implies` (n – 10)(n – 3) = 0
`\implies` n – 10 = 0 or n – 3 = 0
`\implies` n = 10 or n = 3
Thus, the required number of terms to be added is 3 or 10.
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