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Find Four Numbers in Ap Whose Sum is 8 and the Sum of Whose Squares is 216. - Mathematics

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प्रश्न

Find four numbers in AP whose sum is 8 and the sum of whose squares is 216.

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उत्तर

(4, 6, 8, 10) or (10, 8, 6, 4)

 

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पाठ 11: Arithmetic Progression - Exercises 2

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आर. एस. अग्रवाल Mathematics [English] Class 10
पाठ 11 Arithmetic Progression
Exercises 2 | Q 11

संबंधित प्रश्‍न

A spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A of radii 0.5, 1.0 cm, 1.5 cm, 2.0 cm, .... as shown in figure. What is the total length of such a spiral made up of thirteen consecutive semicircles? (Take `pi = 22/7`)

[Hint: Length of successive semicircles is l1, l2, l3, l4, ... with centres at A, B, A, B, ...  respectively.]


Find the sum of the following arithmetic progressions:

−26, −24, −22, …. to 36 terms


If 10 times the 10th  term of an AP is equal to 15 times the 15th  term, show that its 25th term is zero. 


Divide 24 in three parts such that they are in AP and their product is 440.


The first three terms of an AP are respectively (3y – 1), (3y + 5) and (5y + 1), find the value of y .


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.

 


In an A.P. 17th term is 7 more than its 10th term. Find the common difference.


If the common differences of an A.P. is 3, then a20 − a15 is 


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 the sum of n terms of an A.P. is 2n2 + 5n, then its nth term is


Q.7


In a Arithmetic Progression (A.P.) the fourth and sixth terms are 8 and 14 respectively. Find that:
(i) first term
(ii) common difference
(iii) sum of the first 20 terms. 


How many terms of the A.P. 27, 24, 21, …, should be taken so that their sum is zero?


The sum of all two digit odd numbers is ______.


If Sn denotes the sum of first n terms of an AP, prove that S12 = 3(S8 – S4)


Find the sum of the integers between 100 and 200 that are not divisible by 9.


Sum of 1 to n natural number is 45, then find the value of n.


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.


The sum of n terms of an A.P. is 3n2. The second term of this A.P. is ______.


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