Advertisements
Advertisements
प्रश्न
Find the sum of the first 25 terms of an A.P. whose nth term is given by an = 2 − 3n.
Advertisements
उत्तर
Here, we are given an A.P. whose nth term is given by the following expression, `a_n = 2 - 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 the nth term of A.P.
a = 2 - 3(1)
= 2 - 3
= -1
Now, the last term (l) or the nth term is given
`l = a_n = 2 - 3n`
So, on substituting the values in the formula for the sum of n terms of an A.P., we get,
`S_25 = (25/2)[(-1)+2 -3(25)]`
`= (25/2)[1 - 75]`
`= (25/2)(-74)`
`= (25)(-37)`
= -925
Therefore, the sum of the 25 terms of the given A.P. is `S_25 = -925`
APPEARS IN
संबंधित प्रश्न
The ratio of the sums of m and n terms of an A.P. is m2 : n2. Show that the ratio of the mth and nth terms is (2m – 1) : (2n – 1)
Determine the A.P. whose 3rd term is 16 and the 7th term exceeds the 5th term by 12.
If the sum of the first n terms of an AP is 4n − n2, what is the first term (that is, S1)? What is the sum of the first two terms? What is the second term? Similarly, find the 3rd, the 10th, and the nth terms.
Find the sum of first 20 terms of the sequence whose nth term is `a_n = An + B`
Write the next term of the AP `sqrt(2) , sqrt(8) , sqrt(18),.........`
Which term of the AP 21, 18, 15, … is zero?
Find the sum of the first n natural numbers.
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.
If the sum of first n terms of an A.P. is \[\frac{1}{2}\] (3n2 + 7n), then find its nth term. Hence write its 20th term.
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.
Suppose the angles of a triangle are (a − d), a , (a + d) such that , (a + d) >a > (a − d).
Q.18
The ratio of the 11th term to the 18th term of an AP is 2 : 3. Find the ratio of the 5th term to the 21st term, and also the ratio of the sum of the first five terms to the sum of the first 21 terms.
Solve the equation
– 4 + (–1) + 2 + ... + x = 437
Find the sum of first 'n' even natural numbers.
Calculate the sum of 35 terms in an AP, whose fourth term is 16 and ninth term is 31.
Sum of 1 to n natural number is 45, then find the value of n.
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 the 4th and 8th term of an A.P. is 24 and the sum of the 6th and 10th term of the A.P. is 44. Find the A.P. Also, find the sum of first 25 terms of the A.P.
