Advertisements
Advertisements
Question
Find the sum of the first 25 terms of an A.P. whose nth term is given by an = 7 − 3n
Advertisements
Solution
Here, we are given an A.P. whose nth term is given by the following expression, `a_n = 7 - 3n`. We need to find the sum of first 25 terms.
So, here we can find the sum of the n terms of the given A.P., using the formula,
`S_n = (n/2) (a + l)`
Where a = the first term
l = the last term
So, for the given A.P,
The first term (a) will be calculated using n = 1 in the given equation for nth term of A.P.
a = 7 - 3(1)
= 7 - 3
= 4
Now, the last term (l) or the nth term is given
`l = a_n = 7 - 3n`
So, on substituting the values in the formula for the sum of n terms of an A.P., we get,
`S_25= (258/2)[(4) + 7 - 3 (25)]`
`= (25/2) [11 - 75]`
`= (25/2) (-64)`
= (25)(-32)
= -800
Therefore, the sum of the 25 terms of the given A.P. is `S_n = -800`
RELATED QUESTIONS
The houses in a row numbered consecutively from 1 to 49. Show that there exists a value of x such that sum of numbers of houses preceding the house numbered x is equal to sum of the numbers of houses following x.
Find the sum of first 30 terms of an A.P. whose second term is 2 and seventh term is 22
The sum of the first p, q, r terms of an A.P. are a, b, c respectively. Show that `\frac { a }{ p } (q – r) + \frac { b }{ q } (r – p) + \frac { c }{ r } (p – q) = 0`
If the ratio of the sum of the first n terms of two A.Ps is (7n + 1) : (4n + 27), then find the ratio of their 9th terms.
Find the sum of first n odd natural numbers
Find the common difference of an AP whose first term is 5 and the sum of its first four terms is half the sum of the next four terms.
If an denotes the nth term of the AP 2, 7, 12, 17, ..., find the value of (a30 - a20).
Find the sum of all multiples of 9 lying between 300 and 700.
Choose the correct alternative answer for the following question .
In an A.P. first two terms are –3, 4 then 21st term is ...
The sum of the first n terms of an A.P. is 3n2 + 6n. Find the nth term of this A.P.
The sum of the first n terms of an A.P. is 4n2 + 2n. Find the nth term of this A.P.
The sum of first n terms of an A.P. is 3n2 + 4n. Find the 25th term of this A.P.
Q.12
Q.16
Find the sum of the first 10 multiples of 6.
Determine the sum of first 100 terms of given A.P. 12, 14, 16, 18, 20,......
Activity :- Here, a = 12, d = `square`, n = 100, S100 = ?
Sn = `"n"/2 [square + ("n" - 1)"d"]`
S100 = `square/2 [24 + (100 - 1)"d"]`
= `50(24 + square)`
= `square`
= `square`
If the nth term of an AP is (2n + 1), then the sum of its first three terms is ______.
Find the sum of those integers from 1 to 500 which are multiples of 2 as well as of 5.
The students of a school decided to beautify the school on the Annual Day by fixing colourful flags on the straight passage of the school. They have 27 flags to be fixed at intervals of every 2 m. The flags are stored at the position of the middle most flag. Ruchi was given the responsibility of placing the flags. Ruchi kept her books where the flags were stored. She could carry only one flag at a time. How much distance did she cover in completing this job and returning back to collect her books? What is the maximum distance she travelled carrying a flag?
