Arithmetic Progression (A.P.) Multiple Choice Questions 2

This set of Mathematics Online Quiz for Class 11 focuses on “Arithmetic Progression(A.P.) – 2”.

1. If in an A.P., first term is 20, common difference is 2 and n^th term is 42, then find n.
a) 10
b) 11
c) 12
d) 14
View Answer

Answer: c
Explanation: We know, a=20, d=2, a_n=42.
a+(n-1) d = 42 => 20 + 2(n-1) = 42
=>2(n-1) = 42-20=22 => n-1 =11 => n=12.

2. If in an A.P., first term is 20, common difference is 2 and n^th term is 42, then find sum up to n terms.
a) 12
b) 42
c) 352
d) 372
View Answer

Answer: d
Explanation: We know, a=20, d=2, a_n=42.
a+(n-1) d = 42 => 20 + 2(n-1) = 42
=>2(n-1) = 42-20=22 => n-1 = 11 => n=12.
S_n = \(\frac{n}{2}\) (a+l) => S₁₂ = \(\frac{12}{2}\) (20+42) = 6*62 = 372.

3. If general term of an A.P. is 3n then find common difference.
a) 2
b) 3
c) 5
d) 6
View Answer

Answer: b
Explanation: Given, a_n = 3n.
We know, d = a_n-a_n-1 = 3n – 3(n-1) = 3.

Note: Join free Sanfoundry classes at Telegram or Youtube

4. The sum of n terms of two arithmetic progressions are in the ratio (2n + 3):(7n + 5). Find the ratio of their 9^th terms.
a) 4:5
b) 5:4
c) 9:31
d) 31:9
View Answer

Answer: c
Explanation: Let a, a’ be the first terms and d, d’ be the common differences of 2 A.P.’s respectively.
Given, \(\frac{\frac{n}{2}[2a+(n-1)d]}{\frac{n}{2}[2a’+(n-1)d’]} = \frac{2n+3}{7n+5}\)
=>\(\frac{a+(n-1)d/2}{a’+(n-1) d’/2} = \frac{2n+3}{7n+5}\)
If we have to find ratio of 9^th terms then (n-1)/2 =8 => n=17
=>\(\frac{a+8d}{a’+8d’} = \frac{2*17+3}{7*17+5} = \frac{34+3}{119+5} = \frac{36}{124}\) = 9/31.

5. If two numbers are 2 and 6 then find their arithmetic mean.
a) 3
b) 4
c) 5
d) 8
View Answer

Answer: b
Explanation: We know that arithmetic mean of two numbers is given by the average of two numbers i.e. A.M. = (2+6)/2=8/2 = 4.

Take Mathematics - Class 11 Mock Tests - Chapterwise!
Start the Test Now: Chapter 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

6. Insert 4 numbers between 2 and 22 such that the resulting sequence is an A.P.
a) 4, 8, 12, 16
b) 5, 9, 13, 17
c) 4, 10, 15, 19
d) 6, 10, 14, 18
View Answer

Answer: d
Explanation: Let A.P. be 2, A₁, A₂, A₃, A₄, 22.
=>a=2 and a₆ = a+5d = 22 => 2+5*d=22 => d=4.
A₁ = a₂ = a + d = 2 + 4 = 6.
A₂ = A₁ + d = 6 + 4 = 10.
A₃ = 10 + 4 = 14.
A₄ = 14 + 4 = 18.

7. In A.P. 171, 162, 153, ………. Find first negative term.
a) 0
b) -2
c) -6
d) -9
View Answer

Answer: d
Explanation: a=171 and d=162-171 = -9.
a_n<0
=>171+(n-1) (-9) < 0
=>180-9n < 0
=>9n > 180
=>n > 20 => n=21 for first negative term.
First negative term is 171+(20) (-9) = 171-180 = -9

8. In A.P. 171, 162, 153, ………. Find first non-positive term.
a) 0
b) -2
c) -6
d) -9
View Answer

Answer: a
Explanation: a=171 and d=162-171 = -9.
a_n<=0
=>171+(n-1) (-9) <=0
=>180-9n <=0
=>9n >= 180
=> n >= 20 => n=20 for first non-positive term.
First negative term is 171+(19) (-9) = 171-171 = 0.

Sanfoundry Global Education & Learning Series – Mathematics – Class 11.

To practice Mathematics Online Quiz for Class 11, here is complete set of 1000+ Multiple Choice Questions and Answers.

« Prev - Mathematics Questions and Answers – Arithmetic Progression(A.P.) – 1

» Next - Mathematics Questions and Answers – Geometric Progression(G.P.)

Next Steps: