Question 53

2 3 (ii) 4– + 4 – + 4– +... upto n terms n n n a – b 3a – 2b 5a – 3b (iii) + + + ... to 11 terms. a+b a +b a +b 22. Which term of the AP: –2, –7, –12,... will be –77? Find the sum of this AP upto the term –77. 23. If an = 3 – 4n, show that a1 , a2 , a3 ,... form an AP. Also find S20. 24. In an AP, if Sn = n (4n + 1), find the AP. 25. In an AP, if Sn = 3n2 + 5n and ak = 164, find the value of k. 26. If Sn denotes the sum of first n terms of an AP, prove that S12 = 3(S8 –S4) 27. Find the sum of first 17 terms of an AP whose 4th and 9th terms are –15 and –30 respectively. 28. If sum of first 6 terms of an AP is 36 and that of the first 16 terms is 256, find the sum of first 10 terms. 29. Find the sum of all the 11 terms of an AP whose middle most term is 30. 30. Find the sum of last ten terms of the AP: 8, 10, 12,---, 126. 31. Find the sum of first seven numbers which are multiples of 2 as well as of 9. [Hint: Take the LCM of 2 and 9] 32. How many terms of the AP: –15, –13, –11,--- are needed to make the sum –55? Explain the reason for double answer. 33. The sum of the first n terms of an AP whose first term is 8 and the common difference is 20 is equal to the sum of first 2n terms of another AP whose first term is – 30 and the common difference is 8. Find n. 34. Kanika was given her pocket money on Jan 1st, 2008. She puts Re 1 on Day 1, Rs 2 on Day 2, Rs 3 on Day 3, and continued doing so till the end of the month, from this money into her piggy bank. She also spent Rs 204 of her pocket money, and found that at the end of the month she still had Rs 100 with her. How much was her pocket money for the month? 35. Yasmeen saves Rs 32 during the first month, Rs 36 in the second month and Rs 40 in the third month. If she continues to save in this manner, in how many months will she save Rs 2000?