Tiêu đề 06_VII_e-Tec_VOL-2_Additional Prablems_217-227.pdf ✅

e-Techno Text Book IX-Mathematics (Vol-2) 217 PROGRESSIONS Work Sheet-1 1. The next term in the sequence 1 2 5 , , .... 2 3 6 is 1) 2 2) 3 3) 4 4) 1 2. 3, 7, 15, 31, 63, .... 1) 92 2) 115 3) 127 4) 131 3. 121, 225, 361, .... 1) 441 2) 484 3) 529 4) 729 4. Which number would replace question mark in the series 7, 12, 19, ?, 39. 1) 29 2) 28 3) 26 4) 24 5. 1, 2, 3, 6, 9, 18, ...., 54 1) 18 2) 27 3) 36 4) 81 6. 4, 5, 9, 18, 34, ..... 1) 43 2) 49 3) 59 4) 360 7 3, 6, 5, 20, 7, 42, 9, .... 1) 54 2) 60 3) 66 4) 72 8. 0,5,10,15 forms an AP, then its common difference is 1) 5 2) 10 3) 2 4) 0 9. If the first term of an AP is 3 and its common difference is 5, then its nth term is 1) 3 + 5n 2) 5n – 2 3) 3n – 5 4) 3 – 5n 10. If 11, 6 , 1 , – 4 , –9 forms an AP, then its common difference is 1) – 5 2) 4 3) 5 4) – 4 11. 2, 5,8............. forms an AP, then its 12th term is 1) 30 2) 33 3) 35 4) 37 12. If the nth term of AP is 4n – 1 then the 18th term is 1) 72 2) 73 3) 74 4) 71 13. What term of the A.P. 2, 5, 8, ..... is 56 ? 1) 20 2) 21 3) 19 4) 15
IX-Mathematics (Vol-2) e-Techno Text Book 218 14. If the 3rd and 7th terms of an A.P. are 17 and 27 respectively, then the first term of the A.P is 1) 9 2) 12 3) 14 4) 16 15. The nth term of an A.P. whose 6th and 8th terms are 12 and 22 respectively is 1) 7n – 30 2) n2 – 24 3) 5n – 18 4) 4n – 18 16. nth term of 1, 3, 5 . . . . . is 1) 2n + 1 2) 2n – 1 3) 3n – 1 4) n 2 17. If 10 times 10th term is equal to 20 times 20th term then 30th term is 1) 1 2) 2 3) 3 4) 0 18. What is the next term of the AP 2, 8, 18,........ 1) 24 2) 28 3) 30 4) 32 19. The 9th term of an AP is 449 and 449th term is 9. The term which is equal to zero is 1) 501th 2) 502th 3) 458th 4) 459th 20. Which of the following is not an AP? 1) 13,8,3, 2, 7, 12    2) 10.8, 11.2, 11.6, 12, 12.4 3) 1 2 3 4 5 8 ,18 ,28 ,48 , 58 7 7 7 7 7 4) 3 6 9 12 8 ,11 ,14 ,17 23 23 23 23 21. If 3, 10, 17 are in A.P and the nth term is 84 more than the 13th term, then the value of n is 1) 26 2) 24 3) 25 4) 20 COMPREHENSION TYPE: The pth term of an AP is 20 and qth term is 10, then 22. The common difference of AP 1) 10 p q  2) 10 q p 3) 10 p q  4) 10 pq 23. The first term of the given AP 1) 10 2pq p 1   pq   2)       10 2 p q p 1 p q     3) 10 2pq p 1   pq   4) none

IX-Mathematics (Vol-2) e-Techno Text Book 220 15. Key : 3 Sol: T6 = a + 5d = 12 ----------- (1) T8 = a + 7d = 22  2d = 10 or d = 5  a + 25 = 12 (from eq(1)]  a = –13  Tn = –13 + (n – 1)5  Tn = 5n – 18 Alternatively : Check the options. 5n – 18  5 × 6 – 18 = 12 and 5 × 8 – 18 = 22 16. Key : 2 Sol: t n = a + (n – 1) d = 1 + (n – 1)2 = 2n – 1 17. (4) 10(a + 9d) = 20(a + 19d)  10a + 90d = 20a + 380d  – 290d = 10a a = – 29d t 30 = a + 29d t 30 = 296 + 296 = 0  t30 = – 29d + 29d = 0 18. (4) a +12d = 64,a +6d = 34Þ6d = 30;d = 5,a = 4;T = 4+45 = 49 10 Given A.P is 1 2,2 2,3 2,....nextterm4 2 = 16 × 2 = 32 19. (3)a +8d = 449,a +448d =9 d = 1,a = 457,0 = 457+ n-1 -1 n=       458 20. (3) 4 3 3 2 48 28 28 18 7 7 7 7     D is not contant 21. (3) When nth term of the AP 3, 10, 17....... will be 84 more than its 13th term. a = 3, d = 7 t 13 = a + 12d = 3 + 84 = 87 t n = t13 + 84 = 87 + 84 = 171  a + (n – 1)d = 171 3 + (n – 1)7 = 171 3 + 7n – 7 = 171 7n – 4 = 171 7n = 175 n = 25 22. (3) Sol: a + (p –1) d = 20 ..............(1) a + (q –1)d = 10 ...................(2) Substracing (2) from (1) we get 10 d p q   23. (2) a + (p-1)d = 20 ;   10 a p 1 20 p q     