Advertisements
Advertisements
प्रश्न
Find the sum of the following APs.
−37, −33, −29, …, to 12 terms.
Advertisements
उत्तर
−37, −33, −29, …, to 12 terms
For this A.P.,
a = −37
d = a2 − a1
= (−33) − (−37)
= −33 + 37
= 4
n = 12
We know that,
Sn = `n/2 [2a+(n - 1) d]`
S12 = `12/2 [2(-37)+(12 - 1) × 4]`
= 6[-74 + 11 × 4]
= 6[-74 + 44]
= 6(-30)
= -180
Thus, the sum of first 12 terms is -180.
संबंधित प्रश्न
If the 3rd and the 9th terms of an AP are 4 and –8 respectively, which term of this AP is zero?
Find the sum given below:
`7 + 10 1/2 + 14 + ... + 84`
Find the sum of the following arithmetic progressions:
1, 3, 5, 7, ... to 12 terms
Find the sum of the following arithmetic progressions:
41, 36, 31, ... to 12 terms
Find the sum of the first 25 terms of an A.P. whose nth term is given by an = 7 − 3n
If the 12th term of an A.P. is −13 and the sum of the first four terms is 24, what is the sum of first 10 terms?
The first term of an A.P. is 5, the last term is 45 and the sum of its terms is 1000. Find the number of terms and the common difference of the A.P.
The first and the last terms of an A.P. are 34 and 700 respectively. If the common difference is 18, how many terms are there and what is their sum?
Find the 6th term form the end of the AP 17, 14, 11, ……, (-40).
Rs 1000 is invested at 10 percent simple interest. Check at the end of every year if the total interest amount is in A.P. If this is an A.P. then find interest amount after 20 years. For this complete the following activity.
The first and the last terms of an A.P. are 8 and 350 respectively. If its common difference is 9, how many terms are there and what is their sum?
The sum of 5th and 9th terms of an A.P. is 30. If its 25th term is three times its 8th term, find the A.P.
In a school, students decided to plant trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be double of the class in which they are studying. If there are 1 to 12 classes in the school and each class has two sections, find how many trees were planted by the students.
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.
Write the nth term of the \[A . P . \frac{1}{m}, \frac{1 + m}{m}, \frac{1 + 2m}{m}, . . . .\]
x is nth term of the given A.P. an = x find x .
A sum of Rs. 700 is to be paid to give seven cash prizes to the students of a school for their overall academic performance. If the cost of each prize is Rs. 20 less than its preceding prize; find the value of each of the prizes.
If the sum of the first four terms of an AP is 40 and that of the first 14 terms is 280. Find the sum of its first n terms.
The sum of first n terms of an A.P. whose first term is 8 and the common difference is 20 equal to the sum of first 2n terms of another A.P. whose first term is – 30 and the common difference is 8. Find n.
Find the sum of the integers between 100 and 200 that are
- divisible by 9
- not divisible by 9
[Hint (ii) : These numbers will be : Total numbers – Total numbers divisible by 9]
