Mathematics Questions and Answers – Arithmetic Progression(A.P.) – 2

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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 nth 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, an=42.
a+(n-1) d = 42 => 20 + 2(n-1) = 42
=>2(n-1) = 42-20=22 => n-1 =11 => n=12.
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2. If in an A.P., first term is 20, common difference is 2 and nth 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, an=42.
a+(n-1) d = 42 => 20 + 2(n-1) = 42
=>2(n-1) = 42-20=22 => n-1 = 11 => n=12.
Sn = \(\frac{n}{2}\) (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, an = 3n.
We know, d = an-an-1 = 3n – 3(n-1) = 3.
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4. The sum of n terms of two arithmetic progressions are in the ratio (2n + 3):(7n + 5). Find the ratio of their 9th 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 9th 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.
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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.
an<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
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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.
an<=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.

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter