Advertisements
Advertisements
प्रश्न
If the sum of first n terms is (3n2 + 5n), find its common difference.
Advertisements
उत्तर
Let Sn denotes the sum of first n terms of the AP.
∴ sn = 3n2 + 5n
⇒ `s_(n-1) = 3 (n-1) ^2 + 5 (n-1)`
= `3(n^2 - 2n + 1) + 5 (n-1)`
=`3n^2 -n-2`
Now ,
nth term of AP , an = sn - sn-1
= (3n2 + 5n ) - ( 3n2 -n-2)
= 6n + 2
Let d be the common difference of the AP.
∴ d = an - a n-1
= (6n + 2 ) - [ 6(n-1 ) +2]
= 6n + 2 - 6 (n-1) -2
= 6
Hence, the common difference of the AP is 6.
APPEARS IN
संबंधित प्रश्न
A contract on a construction job specifies a penalty for delay of completion beyond a certain date as follows: Rs. 200 for the first day, Rs. 250 for the second day, Rs. 300 for the third day, etc., the penalty for each succeeding day being Rs. 50 more than for the preceding day. How much money does the contractor have to pay as a penalty if he has delayed the work by 30 days.
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`]
Find the sum of the first 15 terms of each of the following sequences having the nth term as
bn = 5 + 2n
Find the 6th term form the end of the AP 17, 14, 11, ……, (-40).
Find the sum of the first n natural numbers.
Find the sum of the following Aps:
i) 2, 7, 12, 17, ……. to 19 terms .
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.
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.
If S1 is the sum of an arithmetic progression of 'n' odd number of terms and S2 the sum of the terms of the series in odd places, then \[\frac{S_1}{S_2} =\]
In an AP. Sp = q, Sq = p and Sr denotes the sum of first r terms. Then, Sp+q is equal to
Q.13
Q.20
How many terms of the A.P. 27, 24, 21, …, should be taken so that their sum is zero?
Solve for x: 1 + 4 + 7 + 10 + ... + x = 287.
In an A.P., the sum of its first n terms is 6n – n². Find is 25th term.
Find second and third terms of an A.P. whose first term is – 2 and the common difference is – 2.
Find S10 if a = 6 and d = 3
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.
If the first term of an A.P. is p, second term is q and last term is r, then show that sum of all terms is `(q + r - 2p) xx ((p + r))/(2(q - p))`.
