Mathematics
Assertion (A): The sum of first n terms of the A.P. −1, 5, 11, … is 3n2 − 4n.
Reason (R): The sum of first n terms of an A.P. is given by Sn = [2a + (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.
AP
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Answer
A.P. : -1, 5, 11, ……
Given,
a = -1
d = 5 - (-1) = 6
We know that,
Sn = [2a + (n − 1)d]
⇒ Sn = [2(-1) + (n − 1)6]
= [-2 + (6n − 6)]
= (6n − 8)
= 2(3n − 4)
= n(3n - 4)
= 3n2 - 4n.
∴ Assertion (A) is true.
The standard and correct formula for the sum of the first n terms of an A.P.
Sn = [2a + (n − 1)d]
∴ Reason (R) is true.
Both A and R are true.
Hence, option 3 is the correct option.
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Related Questions
Case Study II
The production of TV sets in a factory increases uniformly by a fixed number every year.
It produced 16000 sets in the 6th year and 22600 in the 9th year.Based on this information, answer the following questions:
The production of the TV sets during the first year was :
(a) 4000
(b) 4500
(c) 5000
(d) 5500What was the uniform increase in the production of TV sets every year?
(a) 1800
(b) 2400
(c) 1600
(d) 2200The production of the TV sets during the 8th year was:
(a) 20000
(b) 20400
(c) 21200
(d) 22800The total production of the TV sets during first 6 years was:
(a) 56000
(b) 72000
(c) 66000
(d) 63000The average production of the TV sets during first 6 years was:
(a) 10500
(b) 11000
(c) 11500
(d) 12000
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
Assertion (A): For an A.P., T22 = 149 and d = 7. Then S22 is 1661.
Reason (R): The sum of first n terms of an A.P. is given by Sn = .
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false