# NCERT Mathematics Class 10 Exemplar Ch 5 Arithmetic Progressions Part 5

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11. Determine k so that are three consecutive terms of an AP.

Answer:

12. Split 207 into three parts such that these are in AP and the product of the two smaller parts is 4623.

Answer: 67, 69, 71

13. The angles of a triangle are in AP. The greatest angle is twice the least. Find all the angles of the triangle.

Answer:

14. If the nth terms of the two and are the same, find the value of n. Also find that term.

Answer: 16th term; β21

15. If sum of the 3rd and the 8th terms of an AP is 7 and the sum of the 7th and the 14th terms is β3, find the 10th term.

Answer: β1

16. Find the 12th term from the end of the AP:

Answer: β78

17. Which term of the AP: is the first negative term?

Answer: 12^{th} term

18. How many numbers lie between 10 and 300, which when divided by 4 leave a remainder 3?

Answer: 73

19. Find the sum of the two middle most terms of the AP:

Answer: 3

20. The first term of an AP is β5 and the last term is 45. If the sum of the terms of the AP is 120, then find the number of terms and the common difference.

Answer: ,

21. Find the sum: (i)

(ii) upto n terms

(iii) to 11 terms.

Answer: (i) (ii) (iii)

22. Which term of the AP: will be ? Find the sum of this AP upto the term .

Answer: 16^{th} term; β632

23. If , show that form an AP. Also find S_{20} .

Answer:

24. In an AP, if , find the AP.

Answer:

25. In an AP, if and find the value of k.

Answer: