4 Marks Questions

3.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

51

4.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 ​

6 Marks Questions

1. 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)

2.  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)]

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

Ans. 

Sq both side

4. 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.

5. The Sum of two no. is 6 times their geometric mean, show that no. are in the ratio (3 + 3 √2) : (3 – 2 √2)

Ans.