Question 1

Number series (decreasing gaps): Find the next term in 120, 99, 80, 63, 48, ?  Observe the first differences and extend the pattern to compute the missing term. Choose the correct value.

Accepted Answer

Compute first differences 99 − 120 = −21 80 − 99 = −19 63 − 80 = −17 48 − 63 = −15 Pattern Differences increase by +2 each step (−21, −19, −17, −15 …). Next difference and term Next diff = −13 ⇒ Next term = 48 − 13 = 35.

Question 2

Digit-elimination pattern: Identify the next term in 589654237, 89654237, 8965423, 965423, ?  Notice how each successive term is derived by alternately dropping the first and last digit. Determine the next output. Choose the correct value.

Accepted Answer

Step-by-step transformation 589654237 → (drop first digit) → 89654237 89654237 → (drop last digit) → 8965423 8965423 → (drop first digit) → 965423 965423 → (drop last digit) → 96542

Question 3

Recursive squaring pattern: Find the next term in 3, 10, 101, ?  Clue: each term is one more than the square of the previous term. Compute the next term explicitly. Choose the correct value.

Accepted Answer

Recognize the rule an+1 = an2 + 1 Verify 3 → 3² + 1 = 9 + 1 = 10 10 → 10² + 1 = 100 + 1 = 101 Next term 101 → 101² + 1 = 10201 + 1 = 10202

Question 4

Geometric progression (×3): Find the 8th term of the sequence 2, 6, 18, 54, …  Recognize the constant ratio and use the nth-term formula to compute term 8. Choose the correct value.

Accepted Answer

Identify GP Common ratio r = 3; first term a = 2. Apply nth-term Tn = a · rn−1 T8 = 2 · 37 = 2 · 2187 = 4374.

Question 5

Number series (arithmetic step pattern): Find the next term in 125, 80, 45, 20, ?  Observe the steadily increasing (less negative) step differences and continue the pattern. Choose the correct value.

Accepted Answer

Compute differences 80 − 125 = −45 45 − 80 = −35 20 − 45 = −25 Pattern Each step increases by +10 (−45, −35, −25, …), so next step is −15. Next term 20 + (−15) = 5.

Question 6

Interleaved squares and cubes: Determine the missing term in 1, 1, 4, 8, 9, 27, 16, ?  Odd positions are perfect squares (1², 2², 3², 4², …) and even positions are perfect cubes (1³, 2³, 3³, 4³, …). Compute the 8th term. Choose the correct value.

Accepted Answer

Identify the two subsequences Odd indices: 1, 4, 9, 16, … ⇒ 1², 2², 3², 4², … Even indices: 1, 8, 27, … ⇒ 1³, 2³, 3³, … Find the 8th term Position 8 is even ⇒ 4³ = 64.

Question 7

Number series (missing term): Identify the value that correctly continues the alternating multiplication pattern.  Given sequence: 1, 2, 3, 6, 9, 18, ?, 54 Pattern hint: terms alternate between ×2 and ×1.5 (i.e., ×3/2). Choose the correct missing nu…

Accepted Answer

Given data Sequence: 1, 2, 3, 6, 9, 18, ?, 54 Concept/Approach The pattern alternates: multiply by 2, then by 1.5 (i.e., 3/2). Step-by-step 1 × 2 = 22 × 1.5 = 33 × 2 = 66 × 1.5 = 99 × 2 = 1818 × 1.5 = 2727 × 2 = 54 (checks next term) Final Answer 27

Question 8

Number series (find the next term): Use the alternating 2×±1 rule.  Given sequence: 6, 13, 25, 51, 101, ? Observation hint: each term is about double the previous, with alternating +1 and −1. Choose the correct next number.

Accepted Answer

Pattern Apply: next = (2 × previous) ± 1, alternating +1, −1, +1, −1, … Step-by-step 6 → 13: 2×6 + 1 = 1313 → 25: 2×13 − 1 = 2525 → 51: 2×25 + 1 = 5151 → 101: 2×51 − 1 = 101So next: 2×101 + 1 = 203 Final Answer 203

Question 9

Number series (missing term): Differences follow triangular numbers.  Given sequence: 5, 6, 9, 15, ?, 40 Hint: successive differences are 1, 3, 6, 10, 15, … Choose the correct missing number.

Accepted Answer

Observation Differences: 6−5=1, 9−6=3, 15−9=6, ?−15=10, 40−?=15. These are triangular numbers (1, 3, 6, 10, 15 … with increments +2, +3, +4, +5). Compute Missing term = 15 + 10 = 25Check next: 40 − 25 = 15 (fits the pattern) Final Answer 25

Question 10

Number series (next term): Apply a Tribonacci-type recurrence.  Given sequence: 1, 3, 4, 8, 15, 27, ? Hint: each term equals the sum of the previous three terms (Tribonacci). Choose the correct next number.

Accepted Answer

Concept Tribonacci: t(n) = t(n−1) + t(n−2) + t(n−3). Verify 8 = 4 + 3 + 115 = 8 + 4 + 327 = 15 + 8 + 4 Next term t = 27 + 15 + 8 = 50 Final Answer 50

Question 11

Number series (next term): Two interleaved progressions with increasing gaps.  Given sequence: 3, 4, 7, 7, 13, 13, 21, 22, 31, 34, ? Hint: treat odd and even positions separately. Choose the correct next number.

Accepted Answer

Split sequences Odd positions: 3, 7, 13, 21, 31, … differences: +4, +6, +8, +10 ⇒ next odd term = 31 + 12 = 43. Even positions: 4, 7, 13, 22, 34, … differences: +3, +6, +9, +12 (multiples of 3). Next term We need the 11th term (odd-indexed) ⇒ 43.

Question 12

Number series (missing term): Successive subtractions of perfect squares.  Given sequence: 198, 194, 185, 169, ? Hint: subtract 2², 3³? No—subtract squares in order: 4, 9, 16, 25, … Choose the correct missing number.

Accepted Answer

Pattern 198 − 4 = 194 (−2²), 194 − 9 = 185 (−3²), 185 − 16 = 169 (−4²). Next subtract 5² = 25. Compute 169 − 25 = 144 Final Answer 144

Question 13

Number series (identify the prime): Fill the missing prime number.  Given sequence: 2, 3, 5, 7, 11, ?, 17 Choose the correct missing prime.

Accepted Answer

Observation The sequence lists consecutive prime numbers. Next prime after 11 13 Final Answer 13

Question 14

Number series (missing term): Differences increase by a constant step.  Given sequence: 6, 12, 21, ?, 48 Hint: successive differences rise by 3 each time (6, 9, 12, 15, …). Choose the correct missing number.

Accepted Answer

Differences 12 − 6 = 621 − 12 = 9? − 21 = 12 ⇒ ? = 3348 − 33 = 15 (continues the +3 step) Final Answer 33

Question 15

Geometric progression (term index): Find which term equals 1280.  Series definition: 5, 10, 20, 40, … (each term doubles the previous). Determine the term number n for which the value is 1280. Choose the correct index.

Accepted Answer

Model tn = 5 × 2n−1. Solve for n 5 × 2n−1 = 12802n−1 = 1280 / 5 = 256 = 28n − 1 = 8 ⇒ n = 9 Final Answer 9th

Question 16

Number series (fill the blank): Increasing differences by +1 each step.  Given sequence: 2, 5, 9, ?, 20, 27 Hint: differences are 3, 4, 5, 6, 7, … Choose the correct missing number.

Accepted Answer

Differences 5 − 2 = 39 − 5 = 4? − 9 = 5 ⇒ ? = 1420 − 14 = 6, 27 − 20 = 7 (pattern confirmed) Final Answer 14

Question 17

Number series with alternating operations: find the missing term to continue the pattern.  Sequence given: 2, 3, 3, 5, 10, 13, ?, 43, 172, 177 Identify the rule and compute the value of the missing term.  Choose the correct next number.

Accepted Answer

Pattern insight The sequence alternates between “add an increasing odd number” and “multiply by an increasing integer”. Detail Start at 2: +1 → 3; ×1 → 3; +2 → 5; ×2 → 10; +3 → 13; ×3 → 39; +4 → 43; ×4 → 172; +5 → 177. Result The missing term after 13 is 13 × 3 = 39. Common pitfall Assuming a single arithmetic or geometric pattern; it is a mixed-operation pattern.

Question 18

Number series (× and + alternating with growing addends): find the next term.  Sequence given: 9, 27, 31, 155, 161, 1127, ? Identify the alternating operations and compute the next number.  Choose the correct value.

Accepted Answer

Pattern Multiply by an odd number, then add the next even number: ×3, +4, ×5, +6, ×7, +8, … Apply 9 × 3 = 27; 27 + 4 = 31; 31 × 5 = 155; 155 + 6 = 161; 161 × 7 = 1127; 1127 + 8 = 1135.

Question 19

Number sequence (increasing integers with special cases): determine the next term.  Sequence given: 2, 1, 2, 4, 4, 5, 6, 7, 8, 8, 10, 11, ? Infer the inclusion/omission rule and compute the next number.  Choose the correct value.

Accepted Answer

Observation Natural numbers appear in increasing order but odd multiples of 3 (3, 9, 15, …) are omitted. Powers of 2 (2, 4, 8, …) appear twice. Check the run … 7, 8, 8, 10, 11, (skip 9 as it is an odd multiple of 3) → next allowed integer is 12. Note This explains earlier duplications at 2, 4 and 8, and the absence of 3 and 9.

Question 20

Cubes sequence identification: pick the number that does NOT belong to the list of perfect cubes.  Series displayed: 1, 8, 27, 64, 125, … Recognize these as n³ and find the outlier among the options.  Choose the number that is not a perfect cube.

Accepted Answer

Concept 1, 8, 27, 64, 125, … are 1³, 2³, 3³, 4³, 5³, … Check options 512 = 8³ (cube) 729 = 9³ (cube) 1000 = 10³ (cube) 256 = 2⁸ (not a cube)

Series Completion Questions