Maths MCQ Class 10 Ch - 5 | Arithmetic Progression

Mathematics
MCQ | Class 10 | Ch-5 ARITHMATIC PROGRESSION

MCQ | ARITHMETIC PROGRESSION | CLASS 10

Q 1) In an Arithmetic Progression, if a = 28, d = - 4, n = 7, then a_n is:
a) 4
b) 5
c) 3
d) 7 

Ans: a

Q 2) If a = 10 and d = 10, then first four terms will be:
a) 10, 30, 50, 60
b) 10, 20, 30, 40
c) 10, 15, 20, 25
d) 10, 18, 20, 30
Ans: b

Q 3) 30th term of the A.P: 10, 7, 4, …, is
a) 97
b) 77
c) - 77
d) - 87
Ans: c

Q 4) 11th term of the A.P. - 3, -1/2, 2 …. Is
a) 28
b) 22
c) – 38
d) – 48 

Ans: b

Q 5) The missing terms in AP: __, 13, __, 3 are:
a) 11 and 9
b) 17 and 9
c) 18 and 8
d) 18 and 9 

Ans: c

Q 6) Which term of the A.P. 3, 8, 13, 18, … is 78?
a) 12th
b) 13th
c) 15th
d) 16th 

Ans: d

Q 7) The 21st term of AP whose first two terms are -3 and 4 is:
a) 17
b) 137
c) 143
d) -143 

Ans: b

Q 8) The number of multiples of 4 between 10 and 250 is:
a) 50
b) 40
c) 60
d) 30 

Ans: c

Q 9) 20th term from the last term of the A.P. 3, 8, 13, …, 253 is:
a) 147
b) 151
c) 154
d) 158 

Ans: d

Q 10) The sum of the first five multiples of 3 is:
a) 45
b) 55
c) 65
d) 75 

Ans: a

Q 11) In an AP, if d = - 4, n = 7, a_n = 4, then a is
a) 6
b) 7
c) 20
d) 28 

Ans: d

Q 12) The list of numbers –10, –6, –2, 2,… is
a) an AP with d = –16
b) an AP with d = 4
c) an AP with d = –4
d) not an AP 

Ans: b

Q 13) If the 2nd term of an AP is 13 and the 5th term is 25, then its 7th term is
a) 30
b) 33
c) 37
d) 38 

Ans: b

Q 14) Which term of the AP: 21, 42, 63, 84,… is 210?
a) 9th
b) 10th
c) 11th
d) 12th 

Ans: b

Q 15) What is the common difference of an AP in which a₁₈ – a₁₄ = 32?
a) 8
b) – 8
c) – 4
d) 4 

Ans: a

Q 16) The famous mathematician associated with finding the sum of the first 100 natural numbers is
a) Pythagoras
b) Newton
c) Gauss
d) Euclid 

Ans: c

Q 17) The sum of first 16 terms of the AP: 10, 6, 2,… is
a) –320
b) 320
c) –352
d) –400 

Ans: a

Q 18) The nth term of an A.P. is given by an = 3 + 4n. The common difference is
a) 7
b) 3
c) 4
d) 1 

Ans: c

Q 19) If the sum of three numbers in an A.P. is 9 and their product is 24, then numbers are
a) 2, 4, 6
b) 1, 5, 3
c) 2, 8, 4
d) 2, 3, 4 

Ans: d
Explanation: Reason: Let three numbers be a – d, a, a + d
∴ a – d + a + a + d = 9
⇒ 3a = 9 ⇒ a = 3
Also (a – d) . a . (a + d) = 24
⇒ (3 -d) .3(3 + d) = 24
⇒ 9 – d² = 8
⇒ d² = 9 – 8 = 1
∴ d = ± 1
Hence numbers are 2, 3, 4 or 4, 3, 2

Q 20)  The 10th term from the end of the A.P. -5, -10, -15,…, -1000 is
a) – 955
b) – 945
c) – 950
d) – 965 

Ans: a

Q 21) The sum of all two digit odd numbers is
a) 2575
b) 2475
c) 2524
d) 2425 

Ans: b

Q 22) Find the sum of 12 terms of an A.P. whose nth term is given by an = 3n + 4
(a) 262
(b) 272
(c) 282
(d) 292 

Ans: a

Q 23) The sum of first n odd natural numbers is
(a) 2n²
(b) 2n + 1
(c) 2n – 1
(d) n² 

Ans: d

Q 24) The sum of first n terms of the series a, 3a, 5a, …….. is
(a) na
(b) (2n – 1) a
(c) n²a
(d) n²a² 

Ans: c

Q 25) If 2x, x + 10, 3x + 2 are in A.P., then x is equal to
(a) 0
(b) 2
(c) 4
(d) 6 

Ans: d

Q 26) Which term of the AP: 27, 24, 21, ……… is zero?
(a) 8th
(b) 10th
(c) 9th
(d) 11th 

Ans: b

Q 27) If 7 times the 7th term of an A.P. is equal to 11 times its 11th term, then 18th term is
(a) 18
(b) 9
(c) 77
(d) 0 

Ans: d

Q 28) If the 2nd term of an AP is 13 and the 5th term is 25, what is its 7th term?
(a) 30
(b) 33
(c) 37
(d) 38 

Ans: b

Q 29) Next term of the AP √2, 3√2, 5√2, ……. is
(a) 2√7
(6) 6√2
(c) 9√2
(d) 7√2 

Ans: d

Q 30) If p, q, r and s are in A.P. then r – q is
(a) s – p
(b) s – q
(c) s – r
(d) none of these 

Ans: c

Q 31) If the sum of three numbers in an A.P. is 9 and their product is 24, then numbers are
(a) 2, 4, 6
(b) 1, 5, 3
(c) 2, 8, 4
(d) 2, 3, 4 

Ans: d

Q 32) If the sum of the first m terms of an AP is n and the sum of its n terms is m, then the sum of its (m + n) terms will be
(a) m + n
(b) -(m + n)
(c) m – n
(d) 0 

Ans: b

Q 33) The (n – 1)th term of an A.P. is given by 7,12,17, 22,… is
(a) 5n + 2
(b) 5n + 3
(c) 5n – 5
(d) 5n – 3 

Ans: d

Q 34) If a, b, c, d, e are in A.P., then the value of a – 4b + 6c – 4d + e is
(a) 0
(b) 1
(c) -1.
(d) 2
Ans: a 

Explanation : Let common difference of A.P. be d
∴ b = a + d, c = a + 2d, d = a + 3d and e = a + 4d
Given equation a-4b + 6c-4d + c
= a – 4(a + d) + 6(a + 2d) – 4(a + 3d) + (a + 4d)
= a – 4a – 4d + 6a + 12d – 4a – 12d + a + 4d = 8a – 8a + 16d – 16d = 0

Q 35) nth term of the sequence a, a + d, a + 2d,… is
(a) a + nd
(b) a – (n – 1)d
(c) a + (n – 1)d
(d) n + nd 

Ans: a

Q 36) If 2x, x + 10, 3x + 2 are in A.P., then x is equal to
(a) 0
(b) 2
(c) 4
(d) 6 

Ans: d

Q 37) The 10th term from the end of the A.P. 4, 9,14, …, 254 is
(a) 209
(b) 205
(c) 214
(d) 213 

Ans: a

Q 38) If the sum of first n terms of an AP is An + Bn² where A and B are constants. The common difference of AP will be
(a) A + B
(b) A – B
(c) 2A
(d) 2B 

Ans: d

Q 39) The sum of all odd integers between 2 and 100 divisible by 3 is
(a) 17
(b) 867
(c) 876
(d) 786 

Ans: b

Q 40) The sum of the first 15 multiples of 8 is
(a) 920
(b) 860
(c) 900
(d) 960 

Ans: d

Q 41) The 21st term of the AP whose first two terms are –3 and 4 is
(a) 17
(b) 137
(c) 143
(d) –143 

Ans: b

Q 42) If the 2nd term of an AP is 13 and the 5th term is 25, what is its 7th term?
(a) 30
(b) 33
(c) 37 

(d) 38

Ans: b

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