Number Series Practice Set (UGC NET Paper 1)
Q.1: 2, 6, 12, 20, 30, ?
a) 40
b) 42
c) 44
d) 46
Ans: b)
Solution: The difference between consecutive terms is increasing by 2:
6 – 2 = 4; 12 – 6 = 6; 20 – 12 = 8; 30 – 20 = 10
The next difference should be 12. So, $30 + 12 = 42$.
Q.2: 7, 11, 13, 17, 19, 23, ?
a) 25
b) 27
c) 29
d) 31
Ans: c)
Solution: This is a series of consecutive prime numbers. The prime number following 23 is 29.
Q.3: 1, 4, 9, 16, 25, ?
a) 30
b) 35
c) 36
d) 49
Ans: c)
Solution: The terms are squares of natural numbers: 1², 2², 3², 4², 5². The next is 6² = 36.
Q.4: 8, 27, 64, 125, 216, ?
a) 343
b) 512
c) 729
d) 1000
Ans: a)
Solution: The terms are cubes of natural numbers: 2³, 3³, 4³, 5³, 6³. The next is 7³ = 343
Q.5: 3, 6, 11, 18, 27, ?
a) 36
b) 38
c) 40
d) 42
Ans: b)
Solution: The pattern is +3, +5, +7, +9. The next increment is +11. So, 27 + 11 = 38. (Alternatively: n² + 2).
Q.6: 10, 100, 200, 310, ?
a) 400
b) 410
c) 420
d) 430
Ans: d)
Solution: The differences are +90, 100, 110. The next difference is +120. So, 310 + 120 = 430.
Q.7: 0.5, 2, 4.5, 8, 12.5, ?
a) 16
b) 17
c) 18
d) 19
Ans: c)
Solution: The pattern is 0.5 ×n²: 0.5 × 1², 0.5 × 2², 0.5 ×3², 0.5 × 4², 0.5 × 5². Next is 0.5 × 6² = 0.5 ×36 = 18.
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Q.8: 2, 3, 5, 8, 13, 21, ?
a) 29
b) 31
c) 32
d) 34
Ans: d)
Solution: This is a Fibonacci series where each term is the sum of the two preceding terms: 8+13=21, 13+21=34.
Q.9: 120, 99, 80, 63, 48, ?
a) 35
b) 38
c) 39
d) 40
Ans: a)
Solution: The pattern is n² – 1: 11²-1, 10²-1, 9²-1, 8²-1, 7²-1$. Next is 6²-1 = 35.
Q.10: 2, 12, 36, 80, 150, ?
a) 210
b) 252
c) 258
d) 264
Ans: b)
Solution: The pattern is n³ + n²: 1³+1²=2, 2³+2²=12, 3³+3²=36, 4³+4²=80, 5³+5²=150. Next is 6³+6² = 216+36 = 252.
Q.11: 1, 6, 13, 22, 33, ?
a) 44
b) 45
c) 46
d) 47
Ans: c)
Solution: Differences are +5, +7, +9, +11. Next is +13. 33+13 = 46.
Q.12: 5, 9, 17, 29, 45, ?
a) 60
b) 65
c) 68
d) 70
Ans: b)
Solution: Differences are +4, +8, +12, +16. Next is +20. 45+20 = 65.
Q.13: 4, 12, 36, 108, ?
a) 144
b) 216
c) 304
d) 324
Ans: d)
Solution: Each term is multiplied by 3 (Geometric Progression). 108 × 3 = 324.
Q.14: 1, 1, 2, 6, 24, ?
a) 100
b) 120
c) 144
d) 150
Ans: b)
Solution: The pattern is ×1, × 2, × 3, × 4. Next is × 5. 24 × 5 = 120. (Factorial series: 0!, 1!, 2!, 3!, 4!, 5!).
Q.15: 48, 24, 12, 6, ?
a) 1
b) 2
c) 3
d) 4
Ans: c)
Solution: Each term is divided by 2. 6 ÷ 2 = 3.
Q.16: 2, 5, 9, 19, 37, ?
a) 73
b) 75
c) 76
d) 78
Ans: b)
Solution: The pattern is (Previous ×2) + 1, then (Previous × 2) – 1: 2× 2+1=5; 5×2-1=9; 9× 2+1=19; 19× 2-1=37; 37×2+1 = 75.
Q.17: 10, 14, 26, 42, 70, ?
a) 100
b) 102
c) 114
d) 120
Ans: c)
Solution: Pattern is Sum ×1: (10+14) × 1 + 2 = 26 (irregular). Let’s check differences: 4, 12, 16, 28. Better logic: 10+14=24(+2)=26; 14+26=40(+2)=42; 26+42=68(+2)=70. Next: 42+70=112(+2) = 114.
Q.18: 3, 7, 15, 31, 63, ?
a) 92
b) 115
c) 127
d) 131
Ans: c)
Solution: Pattern is 2n + 1: 3×2+1=7, 7× 2+1=15, etc. 63× 2+1 = 127. (Also 2ⁿ – 1 starting from 2²-1).
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Q.19: 1, 8, 27, 16, 125, 36, 343, ?
a) 49
b) 64
c) 81
d) 100
Ans: b)
Solution: Alternate series:
Series 1: 1³, 3³, 5³, 7³
Series 2: 2², 4², 6². Next in series 2 is 8² = 64.
Q.20: 3, 10, 101, ?
a) 10101
b) 10201
c) 10202
d) 11012
Ans: c)
Solution: Pattern is (n² + 1): 3²+1=10; 10²+1=101; 101²2+1 = 10201+1 = 10202.
Q.21: 5, 11, 23, 47, 95, ?
a) 161
b) 191
c) 190
d) 181
Ans: b)
Solution: Pattern is 2n + 1. 95 × 2 + 1 = 191.
Q.22: 13, 35, 57, 79, 911, ?
a) 1110
b) 1112
c) 1113
d) 1315
Ans: c)
Solution: Each term is formed by two consecutive odd numbers: (1,3), (3,5), (5,7), (7,9), (9,11). Next is (11,13) → 1113.
Q.23: 2, 10, 30, 68, 130, ?
a) 210
b) 216
c) 222
d) 240
Ans: c)
Solution: Pattern is n³ + n: 1³+1, 2³+2, 3³+3, 4³+4, 5³+5. Next is 6³+6 = 216+6 = 222.
Q.24: 1, 2, 3, 1, 4, 9, 1, 8, 27, 1, ?, ?
a) 16, 64
b) 16, 81
c) 25, 125
d) 15, 60
Ans: b)
Solution: The number 1 repeats after every two terms. The sequence is (n, n², 1), (n, n³, 1)? No. Look at blocks: (1,2,3), (1,4,9), (1,8,27).
Block 1: 1, 2¹, 3¹
Block 2: 1, 2², 3²
Block 3: 1, 2³, 3³
Block 4: 1, 2⁴, 3⁴ → 1, 16, 81.
Q.25: 6, 13, 28, 59, ?
a) 111
b) 118
c) 120
d) 122
Ans: d)
Solution: Pattern is 2n + 1, 2n + 2, 2n + 3…:
6× 2+1=13; 13× 2+2=28; 28× 2+3=59; 59× 2+4 = 118+4 = 122.
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