Advertisements
Advertisements
Question
Find the sum 25 + 28 + 31 + ….. + 100
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
25 + 28 + 31 + ….. + 100
Common difference of the A.P. (d) = `a_2 - a_1`
= 28 - 25
= 3
So here,
First term (a) = 25
Last term (l) = 100
Common difference (d) = 3
So, here the first step is to find the total number of terms. Let us take the number of terms as n.
Now, as we know,
`a_n = a + (n -1)d`
So, for the last term,
100 = 25 + (n -1)(3)
100 = 25 + 3n - 3
100 = 22 + 3n
100 - 22 = 3n
Further solving for n,
78 = 3n
`n = 78/3`
n = 26
Now, using the formula for the sum of n terms, we get
`S_n = 26/2[2(25) = (26 - 1)(3)]`
= 13[50 + (25)(3)]
= 13(50 + 75)
= 13(125)
On further simplification, we get,
`S_n = 1625`
Therefore, the sum of the A.P is `S_n = 1625`
APPEARS IN
RELATED QUESTIONS
Divide 32 into four parts which are in A.P. such that the product of extremes is to the product of means is 7 : 15.
In an AP given d = 5, S9 = 75, find a and a9.
Find the sum of the first 15 terms of each of the following sequences having the nth term as
`a_n = 3 + 4n`
The first three terms of an AP are respectively (3y – 1), (3y + 5) and (5y + 1), find the value of y .
How many three-digit natural numbers are divisible by 9?
How many terms of the AP 21, 18, 15, … must be added to get the sum 0?
Kargil’s temperature was recorded in a week from Monday to Saturday. All readings were in A.P. The sum of temperatures of Monday and Saturday was 5°C more than sum of temperatures of Tuesday and Saturday. If temperature of Wednesday was –30° celsius then find the temperature on the other five days.
Divide 207 in three parts, such that all parts are in A.P. and product of two smaller parts will be 4623.
The sum of first n terms of an A.P. is 3n2 + 4n. Find the 25th term of this A.P.
Write 5th term from the end of the A.P. 3, 5, 7, 9, ..., 201.
Write the nth term of an A.P. the sum of whose n terms is Sn.
If Sr denotes the sum of the first r terms of an A.P. Then , S3n: (S2n − Sn) is
If the first term of an A.P. is 2 and common difference is 4, then the sum of its 40 terms is
Q.1
Q.2
Find the sum of first 20 terms of an A.P. whose first term is 3 and the last term is 57.
For an A.P., If t1 = 1 and tn = 149 then find Sn.
Activitry :- Here t1= 1, tn = 149, Sn = ?
Sn = `"n"/2 (square + square)`
= `"n"/2 xx square`
= `square` n, where n = 75
The first term of an AP is –5 and the last term is 45. If the sum of the terms of the AP is 120, then find the number of terms and the common difference.
Jaspal Singh repays his total loan of Rs. 118000 by paying every month starting with the first instalment of Rs. 1000. If he increases the instalment by Rs. 100 every month, what amount will be paid by him in the 30th instalment? What amount of loan does he still have to pay after the 30th instalment?
The sum of 41 terms of an A.P. with middle term 40 is ______.
