Mathematics
Assertion (A): If the sum of first n terms of an A.P. is given Sn = 2n2 − n, then its nth term is 4n + 3.
Reason (R): The nth term (tn) of an A.P. is given by Sn − Sn + 1.
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false
Answer
We know that,
Tn = Sn - Sn - 1
Given,
Sn = 2n2 - n
Sn - 1 = 2(n - 1)2 - (n - 1)
= 2(n2 - 2n + 1) - n + 1
= 2n2 - 4n + 2 - n + 1
= 2n2 - 5n + 3.
Tn = 2n2 - n - (2n2 - 5n + 3)
= 2n2 - n - 2n2 + 5n - 3
= 4n - 3.
Assertion (A) is false.
The nth term of an A.P. is given by,
Tn = Sn - Sn - 1 is correct.
Reason (R) is false.
Both A and R are false.
Hence, option 4 is the correct option.
Related Questions
Case Study III
200 logs are stacked in the following manner:
20 logs in the bottom row, 19 in the next row, 18 in the next row and so on.Based on this information, answer the following questions:
In how many rows these 200 logs are placed?
(a) 25
(b) 20
(c) 16
(d) 14The number of logs in the top row is:
(a) 1
(b) 5
(c) 3
(d) 8The number of logs in the 8th row from the bottom is:
(a) 14
(b) 11
(c) 12
(d) 13Total number of logs in the first six rows from the bottom is:
(a) 105
(b) 95
(c) 85
(d) 75The number of logs in the 5th row from the top is:
(a) 8
(b) 9
(c) 7
(d) 10
Assertion (A): The 10th term from the end of the A.P. 17, 14, 11, … −40 is −11.
Reason (R): The nth term of an A.P. is given by tn = a + (n − 1)d.
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false