Advertisements
Advertisements
Question
Find the sum of the following arithmetic progressions:
3, 9/2, 6, 15/2, ... to 25 terms
Advertisements
Solution
In the given problem, we need to find the sum of terms for different arithmetic progressions. So, here we use the following formula for the sum of n terms of an A.P.,
`S_n = n/2[2a + (n -1)d]`
Where; a = first term for the given A.P
d = common difference of the given A.P.
n = number of terms
3, 9/2, 6, 15/2, ... to 25 terms
Common difference of the A.P. (d) = `a_2 - a_1`
`= 9/2 - 3`
`= (9 - 6)/2`
`= 3/2`
Number of terms (n) = 25
The first term for the given A.P. (a) = 3
So, using the formula we get,
`S_25 = 25/2 [2(3) +(25 - 1)(3/2)]`
`= (25/2)[6 + (25)(3/2)]`
`= (25/2)[6 + (72/2)]`
`= (25/2) [42]`
= 525
On further simplifying we get
`S_25 = 252`
Therefore the sum of first 25 term for the given A.P. is 525
APPEARS IN
RELATED QUESTIONS
Find four numbers in A.P. whose sum is 20 and the sum of whose squares is 120
If the 3rd and the 9th terms of an AP are 4 and –8 respectively, which term of this AP is zero?
In an AP, given a = 2, d = 8, and Sn = 90, find n and an.
In a school, students thought of planting 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 the same as the class, in which they are studying, e.g., a section of class I will plant 1 tree, a section of class II will plant 2 trees, and so on till class XII. There are three sections of each class. How many trees will be planted by the students?
A ladder has rungs 25 cm apart. (See figure). The rungs decrease uniformly in length from 45 cm at the bottom to 25 cm at the top. If the top and bottom rungs are 2 `1/2` m apart, what is the length of the wood required for the rungs?
[Hint: number of rungs = `250/25+ 1`]
If the nth term of the A.P. 9, 7, 5, ... is same as the nth term of the A.P. 15, 12, 9, ... find n.
Find the 12th term from the end of the following arithmetic progressions:
3, 5, 7, 9, ... 201
Three numbers are in A.P. If the sum of these numbers is 27 and the product 648, find the numbers.
Find the sum of the first 40 positive integers divisible by 3
Find the sum of the first 40 positive integers divisible by 5
If `4/5 `, a, 2 are in AP, find the value of a.
The sum of the first n terms of an AP is given by `s_n = ( 3n^2 - n) ` Find its
(i) nth term,
(ii) first term and
(iii) common difference.
There are 37 terms in an A.P., the sum of three terms placed exactly at the middle is 225 and the sum of last three terms is 429. Write the A.P.
If m times the mth term of an A.P. is eqaul to n times nth term then show that the (m + n)th term of the A.P. is zero.
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.
The first and last terms of an A.P. are 1 and 11. If the sum of its terms is 36, then the number of terms will be
The common difference of the A.P.
How many terms of the A.P. 24, 21, 18, … must be taken so that the sum is 78? Explain the double answer.
The sum of first 16 terms of the AP: 10, 6, 2,... is ______.
Find the sum of all the 11 terms of an A.P. whose middle most term is 30.
