Advertisements
Advertisements
प्रश्न
How many terms of the series 18 + 15 + 12 + ........ when added together will give 45?
Advertisements
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.
संबंधित प्रश्न
How many terms are there in the A.P. whose first and fifth terms are −14 and 2 respectively and the sum of the terms is 40?
Find the middle term of the AP 10, 7, 4, ……., (-62).
There are 25 trees at equal distances of 5 metres in a line with a well, the distance of the well from the nearest tree being 10 metres. A gardener waters all the trees separately starting from the well and he returns to the well after watering each tree to get water for the next. Find the total distance the gardener will cover in order to water all the trees.
If the sum of first n even natural numbers is equal to k times the sum of first n odd natural numbers, then k =
If \[\frac{1}{x + 2}, \frac{1}{x + 3}, \frac{1}{x + 5}\] are in A.P. Then, x =
Q.16
Q.18
The sum of first n terms of the series a, 3a, 5a, …….. is ______.
Assertion (A): a, b, c are in A.P. if and only if 2b = a + c.
Reason (R): The sum of first n odd natural numbers is n2.
The sum of n terms of an A.P. is 3n2. The second term of this A.P. is ______.
