RD Sharma Solutions Chapter 9 Arithmetic Progression Exercise 9.4 Class 10 Maths
Chapter Name  RD Sharma Chapter 9 Arithmetic Progression 
Book Name  RD Sharma Mathematics for Class 10 
Other Exercises 

Related Study  NCERT Solutions for Class 10 Maths 
Exercise 9.4 Solutions
1. The sum of three terms of an A.P. is 21 and the product of the first and the third terms exceeds the second term by 6, find three terms.
Solution
Given,
Sum of three terms of on A.P. is 21.
Product of first and the third term exceeds the second term by 6.
Let, the three numbers be a d, a, a +d, with common difference d: then,
2. Three numbers are in A.P. If the sum of these numbers be 27 and the product 648, find the numbers.
Solution
Let, the three numbers are a  d, a, a +d.
Given,
(a  d) + a + (a + d) = 27
3a = 27
a = 27/3 = 9
and, (a d )(a) (a + d) = 648
∴ The three terms are a  d, a + d i.e., 6,9, 12.
3. Find the four numbers in A.P., whose sum is 50 and in which the greatest number is 4 times the least.
Solution
Let, the four numbers be a  3d, a  d, a +d, a + 3d, with common difference 2d.
Given, sum is 50.
4. The angles of a quadrilateral are in A.P. whose common difference is 10°. Find the angles.
Let, the four angles be, a  3d, ad, a +d, a + 3d with common difference = 2d.
2d = 10
d = 10/2 = 5
In a quadrilateral, sum of all angles = 360°
(a  3d) + (a  d) + (a + d) + (a+ 3d) = 360
⇒ 4a = 360
⇒ a = 360/4 = 90°
i.e. 90  3(5), 90  5 , 90 + 5, 90 + 3(5)
= 75°, 85°, 95°, 105°
8x + 4, 6x  2, 2x + 7 are A.P.
Then, 2(6x  2) = 8x + 4 + 2x + 7
12x  4 = 10 + 11
⇒ 2x = 15
⇒ x = 15/2
x + 1, 3x, 4x + 2 are in A.P
If a, b, c are in AP then 2b = a + c
Then 2(3x) = x + 1 + 4x + 2
6x = 5x + 3
⇒ x = 3
If they are in AP. Then they have to satisfy the condition
2b = a + c