NCERT MOST IMPORTANT QUESTIONS CLASS – 11 | MATHS IMPORTANT QUESTIONS | CHAPTER – 9 | SEQUENCES AND SERIES | EDUGROWN |

In This Post we are  providing Chapter-9 SEQUENCES AND SERIES NCERT MOST IMPORTANT QUESTIONS for Class 11 MATHS which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MOST IMPORTANT QUESTIONS ON SEQUENCES AND SERIES

1. A side of an equilateral triangle is 20 cm long. A second equilateral triangle is inscribed in it by joining the mid-points of the sides of the first triangle. This process is continued for third, fourth, fifth, triangles. Find the perimeter of the sixth inscribed equilateral triangle.

Sol: Let the given equilateral triangle be ∆ ABC with each side of 20 cm.
By joining the mid-points of this triangle, we get another equilateral triangle of side equal to half of the length of side of ∆ABC.
Continuing in this way, we get a set of equilateral triangles with side equal to half of the side of the previous triangle.
Now,
Perimeter of first triangle = 20 x 3 = 60 cm;
Perimeter of second triangle = 10 x 3 = 30 cm;
Perimeter of third triangle = 5×3 = 15 cm;

2. In a potato race 20 potatoes are placed in a line at intervals of 4 m with the first potato 24 m from the starting point. A contestant is required to bring the potatoes back to the starting place one at a time. How far would he run in bringing back all the potatoes?
Sol: Distance travelled to bring first potato = 24 + 24 = 2 x 24 = 48 m
Distance travelled to bring second potato = 2(24 + 4) = 2 x 28 = 56 m
Distance travelled to bring third potato = 2(24 + 4 + 4) = 2 X 32 = 64 m; and so on…
Clearly, 48, 56, 64,… is an A.P. with first term 48 and common difference 8. Also, number of terms is 20.
Total distance run in bringing back all the potatoes,

3. Find the rth term of an A.P. sum of whose first n terms is 2n +3n²

Sol: Sum of k terms of A.P., S_n = 2n + 3n²

4. 1f the sum of p terms of an AP. is q and the sum of q terms is p, then show that the sum of p + q terms is —(p + q). Also, find the sum of first p — q terms (where, p > q).

Sol: Let first term and common difference of the A.P. be a and d, respectively. Given, S_p = q

5. If 9 times the 9th term of an A.P. is equal to 13 times the 13th term, then the 22nd term of the A.P. is

Sol:  Let the first term and common difference of given A.P. be a and d, respectively.

6. If x, 2y and 3z are in A.P. where the distinct numbers x, y and z are in G.P., then the common ratio of the G.P.is

Sol: Since x, 2y and 3z are in A.P., we get

7. Let S_n denote the sum of the first n terms of an A.P. If S_2n = 3S_n, then S_3n : S_n  is equal to
Sol Let first term be a and common difference be d.
Then, S_2n = 3S_n

8. If a, b and c are in G.P., then the value of a−bb−c is equal to _________
Sol: Given that, a, b and c are in G.P.

9. Every progression is a sequence but the converse, i.e., every sequence is also a progression need not necessarily be true.
Sol:

 True                                                            –
Consider the progression a, a + d, a + 2d, … and sequence of prime number 2, 3, 5, 7, 11,…
Clearly, progression is a sequence but sequence is not progression because it does not follow a specific pattern.

10.Find the sum to n terms of the series 

33 ​ 34

Ans.a_n = 1² + 2² + 3² + — +n²

35 ​ 36

37 ​ 38

39 ​ 40

41 ​ 42

43 ​ 44

45 ​ 46

47 ​ 48

49 ​ 50

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51

11.Show that the sum of (m+n)^th and (m-n)^th terms of an A. P. is equal to twice the m^th term.

52 ​ 53

Ans. a_m+n = a + (m+n-1) d

54 ​

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6 Marks Questions

12. 150 workers were engaged to finish a job in a certain no. of days 4 workers dropped out on the second day, 4 more workers dropped out on the third day and so on. It took 8 more days to finish the work find the no. of days in which the work was completed  

Ans. a = 150, d = -4 

If total works who would have worked all n days 150(n-8)

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13.  Prove that the sum to n terms of the series 

Ans. Sn = 11 + 103 + 1005 + —- + n terms

Sn = (10+1) + (102 + 3) + (103 + 5) + —– + [10n + (2n-1)]

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14. The ratio of A M and G. M of two positive no. a and b is m : n show that

Ans. 

Sq both side

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15. Between 1 and 31, m number have been inserted in such a way that the resulting sequence is an A.P. and the ratio of 7th and (m-1)th no. is 5:9 find the value of m.

Ans.

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