Question 24: The sum of four consecutive numbers in an AP is 32 and the ratio of the product of the first and the last term to the product of two middle terms is 7 : 15. Find the numbers.

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Let the 4 numbers in AP be x - 3d, x - d, x + d and x + 3d, where 2d is the common difference

__Given Data__: Sum of the 4 numbers is 32.

Sum of 4 numbers = (x - 3d) + (x - d) + (x + d) + (x + 3d) = 4x

4x = 32 or x = 8

∴ The 4 numbers are = (8 - 3d), (8 - d), (8 + d), and (8 + 3d)

Product of first and last term = (8 - 3d) (8 + 3d) = 64 – 9d^{2}

Product of the 2 middle terms = (8 - d) (8 + d) = 64 – d^{2}

__Given Data__: The ratio of the product of the first and the last term to the product of two middle terms is 7 : 15

\\frac{64 - 9d^2}{64 - d^2}) = \\frac{7}{15})

15(64 – 9d^{2}) = 7(64 - d^{2})

15 × 64 - 135d^{2} = 7 × 64 - 7d^{2}

8 × 64 = 128d^{2}

d^{2} = \\frac{8 × 64}{128}) = 4

∴ d = ± 2

If d = 2, the terms are (8 – 3 × 2) + (8 - 2) + (8 + 2) + (8 + 3 × 2)

2, 6, 10, 14.

If d = -2, the terms are (8 – 3 × (-2)) + (8 - (-2)) + (8 + (-2)) + (8 + 3 × (-2))

14, 10, 6, 2.

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CBSE Class 10 Maths - 2022

- Real Numbers Revision Class
- Polynomials Revision Videos
- Linear Equations Revision Class
- Quadratic Equations Revision Class
- Arithmetic Progressions Revision Video
- Triangles Revision
- Coordinate Geometry Revision
- Trigonometry Revision Class
- Appl of Trigonometry
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1. Section A | 2018 CBSE Class 10 Maths 1 Mark **Questions 1 to 6**

2. Section B | 2018 CBSE Class 10 Maths 2 Mark **Question 7** | Real Numbers - Irrational Numbers

3. Section B | 2018 CBSE Class 10 Maths 2 Mark **Question 8** | Linear Equations in 2 variables

4. Section B | 2018 CBSE Class 10 Maths 2 Mark **Question 9** | Sum of Arithmetic Progressions

5. Section B | 2018 CBSE Class 10 Maths 2 Mark **Question 10** | Coordinate Geometry Section Formula

6. Section B | 2018 CBSE Class 10 Maths 2 Mark **Question 11** | Probability of Rolling 2 dice

7. Section B | 2018 CBSE Class 10 Maths 2 Mark **Question 12** | Probability of selecting numbers

8. Section C | 2018 CBSE Class 10 Maths 3 Mark **Question 13** | Real Numbers - LCM & HCF

9. Section C | 2018 CBSE Class 10 Maths 3 Mark **Question 14** | Polynomial Factorization

10. Section C | 2018 CBSE Class 10 Maths 3 Mark **Question 15A** | Coordinate Geometry - Parallelogram

11. Section C | 2018 CBSE Class 10 Maths 3 Mark **Question 15B** | Coordinate Geometry - Area of Triangles

12. Section C | 2018 CBSE Class 10 Maths 3 Mark **Question 16** | Quadratic Equations - Speed Time Distance

13. Section C | 2018 CBSE Class 10 Maths 3 Mark **Question 17** | Similar & Congruent Triangles

14. Section C | 2018 CBSE Class 10 Maths 3 Mark **Question 19** | Trigonometric Ratios

15. Section C | 2018 CBSE Class 10 Maths 3 Mark **Question 20** | Areas related to circles - sector area

16. Section C | 2018 CBSE Class 10 Maths 3 Mark **Question 21** | Surface Areas & Volumes - Cylinder, hemisphere and cone

17. Section C | 2018 CBSE Class 10 Maths 3 Mark **Question 22** | Statistics - Median

18. Section D | 2018 CBSE Class 10 Maths 4 Mark **Question 23** | Quadratic Equations _ Speed Distance Time

19. Section D | 2018 CBSE Class 10 Maths 4 Mark **Question 24** | Arithmetic Progressions

20. Section D | 2018 CBSE Class 10 Maths 4 Mark **Question 25A** | Equilateral & Right Triangles and Congruence

21. Section D | 2018 CBSE Class 10 Maths 4 Mark **Question 25B** | Pythagoram Theorem Proof

22. Section D | 2018 CBSE Class 10 Maths 4 Mark **Question 27** | Trigonometric Ratios & Identities

23. Section D | 2018 CBSE Class 10 Maths 4 Mark **Question 28** | Surface Area of Frustum

24. Section D | 2018 CBSE Class 10 Maths 4 Mark **Question 29** | Applications of Trigonometry - Heights & Distances

25. Section D | 2018 CBSE Class 10 Maths 4 Mark **Question 30** | Statistics - 2 Alternatives

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