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

«
»

This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Arithmetic Progression(A.P.) – 1”.

1. A sequence is called ___________________ if an+1 = an + d.
a) arithmetic progression
b) geometric Progression
c) harmonic Progression
d) special Progression
View Answer

Answer: a
Explanation: A sequence is called arithmetic progression if an+1 = an + d where a1 is the first term and d is common difference.
advertisement

2. What is nth term of an A.P.?
a) an = a + (n-1) d
b) an = a + (n) d
c) an = a*rn-1
d) an = a*rn
View Answer

Answer: a
Explanation: Since every term of an A.P. is incremented by common difference d.
i.e. an+1 = an + d = an-1 + 2d = ……. = a1 + n*d
or an = a + (n-1) d

3. If an A.P. is 3,5,7,9……. Find the 12th term of the A.P.
a) 12
b) 21
c) 22
d) 25
View Answer

Answer: d
Explanation: From the given A.P., a=3 and d=5-3 =2.
We know, an= a + (n-1) d => a12 = a+11d = 3+11*2 = 3+22 = 25.
advertisement
advertisement

4. If a constant is added or subtracted from each term of an A.P. then resulting sequence is also an A.P.
a) True
b) False
View Answer

Answer: a
Explanation: Let x be the constant which is added to each term of an A.P., then an’ = an + x and a’ = a + x. So nth term will be an’ = an + x = a+(n-1) d + x = (a + x) + (n-1) d = a’ + (n-1) d which is nth term of an A.P. If x is negative it is case of subtraction.

5. If a constant is multiplied to A.P. then resulting sequence is also an A.P.
a) True
b) False
View Answer

Answer: a
Explanation: Let x be the constant which is multiplied to each term of an A.P., then an’ = an * x and a’ = a * x. So nth term will be an’ = an * x = (a+(n-1) d) * x = (a * x) + (n-1) d x = a’ + (n-1) x d which is nth term of an A.P.
advertisement

6. If 3rd term of an A.P. is 6 and 5th term of that A.P. is 12. Then find the 21st term of that A.P.
a) 40
b) 42
c) 60
d) 63
View Answer

Answer: c
Explanation: Given, a3 = 6 and a5 = 12.
=> a + 2d = 6 and a + 4d = 12
=> 2d = 6 => d=3.
=> a + 2*3 = 6 => a=0
So, a21 = a + 20 d = 0 + 20*3 = 60.

7. If sum of n terms of an A.P. is n2+5n then find general term.
a) n+1
b) 2n
c) 3n
d) n2+3n
View Answer

Answer: b
Explanation: Given, Sn = n2+5n
We know, an = Sn– Sn-1 = (n2+5n) – ((n-1)2+5(n-1)) = (n2+5n) – (n2+1-2n+5n-1) = 2n.
advertisement

8. If an A.P. is 1,7,13, 19, ……… Find the sum of 22 terms.
a) 127
b) 1204
c) 1408
d) 1604
View Answer

Answer: c
Explanation: From the given A.P., a=1 and d=7-1 = 6.
We know, Sn = \(\frac{n}{2} (2a+(n-1)d)\)
S22 = \(\frac{22}{2} (2*1+(22-1)6)\) = 11(2+21*6) = 11(2+126) = 11*128 = 1408.

9. If in an A.P., first term is 20 and 12th term is 120. Find the sum up to 12th term.
a) 420
b) 840
c) 140
d) 1680
View Answer

Answer: b
Explanation: Given, a=20, a12= 120, n=12.
Sn = \(\frac{n}{2}\) (a+l) => S12 = \(\frac{12}{2} (20+120)\) = 6*140 = 840.
advertisement

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

To practice all areas of Mathematics, here is complete set of 1000+ Multiple Choice Questions and Answers.

Participate in the Sanfoundry Certification contest to get free Certificate of Merit. Join our social networks below and stay updated with latest contests, videos, internships and jobs!

advertisement
advertisement
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