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प्रश्न
How many terms of the series 18 + 15 + 12 + ........ when added together will give 45?
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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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संबंधित प्रश्न
In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato and other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line.
A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?
[Hint: to pick up the first potato and the second potato, the total distance (in metres) run by a competitor is 2 × 5 + 2 × (5 + 3)]
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