Question 1

Interleaved arithmetic progressions (+11): find the missing term in the two intertwined sequences.  Series given: 13, 32, 24, 43, 35, ?, 46, 65, 57, 76 Observe that odd and even positions each form an AP with common difference +11.  Compute the miss…

Accepted Answer

Split positions Odd positions: 13, 24, 35, 46, 57 → add 11 each time. Even positions: 32, 43, ?, 65, 76 → also add 11. Compute 32 → 43 (+11) → 54 (+11) → 65 (+11) → 76.

Question 2

Add successive powers of 2: complete the number series by identifying the additive pattern.  Sequence given: 22, 24, 28, ?, 52, 84 The increments are 2, 4, 8, 16, 32, … (doubling each time).  Find the missing term.

Accepted Answer

Compute step-by-step 22 + 2 = 24 24 + 4 = 28 28 + 8 = 36 36 + 16 = 52 52 + 32 = 84

Question 3

Number series with increasing differences (+8 each step): find the missing term.  Sequence given: 3, 15, ?, 63, 99, 143 Identify the first differences and continue the pattern to fill the blank.  Choose the correct value.

Accepted Answer

First differences 15 − 3 = 12 (?) − 15 = 20 63 − (?) = 28 99 − 63 = 36 143 − 99 = 44 Pattern Differences increase by 8: 12, 20, 28, 36, 44, … Compute 15 + 20 = 35; then 35 + 28 = 63, matching the series.

Question 4

Composite patterned series (doubling blocks interlaced with small reducers): determine the missing value.  Segmented sequence: 90, 180, 12, 50, 100, 200, ?, 3, 50, 4, 25, 2, 6, 30, 3 Notice “doubling runs” (50→100→200) interleaved with small collaps…

Accepted Answer

Structure the line We see a clear doubling subsequence: 50 → 100 → 200 (×2 each step). After this “large build”, the next entry collapses to a small number: the very next term is 3. Consistent link Choosing ? = 150 makes the immediate collapse intelligible: 150 ÷ 50 = 3, and the divisor 50 explicitly appears right after 3 in the list, preserving a neat \“value → reduced result → named divisor\” motif. Why other choices fail 175, 225, or 250 do not yield an integer quotient of 3 with the subsequently displayed number 50 (e.g., 225 ÷ 50 = 4.5, not 3).

Question 5

Alternating ×4 and ÷2 pattern: complete the sequence.  Series given: 48, 24, 96, 48, 192, ? Identify the repeating two-step rule and compute the next term.  Choose the correct number.

Accepted Answer

Rule Alternate between ÷2 and ×4. Apply 48 ÷ 2 = 24; 24 × 4 = 96; 96 ÷ 2 = 48; 48 × 4 = 192; 192 ÷ 2 = 96.

Question 6

Number series with differences as consecutive multiples of 13: find the next term.  Sequence given: 2, 15, 41, 80, ? Observe that consecutive differences are 13, 26, 39, … and continue the pattern.  Choose the correct value.

Accepted Answer

Compute differences 15 − 2 = 13 = 1×13 41 − 15 = 26 = 2×13 80 − 41 = 39 = 3×13 Next step Add 4×13 = 52 to 80 → 80 + 52 = 132.

Question 7

Number series (next term): Increasing differences by a constant step of 5.  Given sequence: 6, 11, 21, 36, 56, ? Identify the missing number that continues the pattern. Choose the correct value.

Accepted Answer

Given data Sequence: 6, 11, 21, 36, 56, ? Concept/Approach Look at first differences; if those grow with a fixed increment, extend the pattern. Step-by-step calculation 11 − 6 = 521 − 11 = 1036 − 21 = 1556 − 36 = 20Next difference = 25 (adds +5 each time)Missing term = 56 + 25 = 81 Verification/Alternative Differences: 5, 10, 15, 20, 25 → arithmetic progression with d = 5. Common pitfalls Confusing with multiplication; it is a simple second-order linear pattern. Final Answer 81

Question 8

Number series (next term): Alternating differences doubling in magnitude with sign flip.  Given sequence: 563, 647, 479, 815, ? Find the next number using the alternating ± pattern on differences. Choose the correct value.

Accepted Answer

Given data 563, 647, 479, 815, ? Concept/Approach Examine successive differences; they alternate sign and double in magnitude. Step-by-step calculation 647 − 563 = +84479 − 647 = −168 = −2×84815 − 479 = +336 = +2×168Next difference = −672 = −2×336Missing term = 815 − 672 = 143 Verification Pattern holds: +84, −168, +336, −672 (×2 each time, signs alternate). Final Answer 143

Question 9

Number series (concatenated odd pairs): Continue the side-by-side odd-number progression.  Given sequence: 13, 35, 57, 79, 911, ? Identify the next concatenated pair of consecutive odd numbers. Choose the correct value.

Accepted Answer

Observation Each term is formed by writing two consecutive odd numbers side by side: 1 and 3 → 13 3 and 5 → 35 5 and 7 → 57 7 and 9 → 79 9 and 11 → 911 Next pair 11 and 13 → 1113 Common pitfalls Interpreting 911 as a single pattern jump; it is 9 concatenated with 11.

Question 10

Number series (next term): Multiply by 2 and add 2 (repeated linear recurrence).  Given sequence: 1, 4, 10, 22, 46, ? Apply the same rule to find the next term. Choose the correct value.

Accepted Answer

Pattern t(n) = 2×t(n−1) + 2 Step-by-step calculation 1 → 2×1+2 = 44 → 2×4+2 = 1010 → 2×10+2 = 2222 → 2×22+2 = 4646 → 2×46+2 = 94 Final Answer 94

Question 11

Number series (next term): Product of digits of the previous term.  Given sequence: 66, 36, 18, ? Use the digit-product rule to continue the series. Choose the correct value.

Accepted Answer

Observation Each term equals the product of the digits of the previous term. Step-by-step calculation 66 → 6×6 = 3636 → 3×6 = 1818 → 1×8 = 8 Common pitfalls Assuming constant ratio or difference; the rule is digit-wise multiplication.

Question 12

Arithmetic progression (nth term): Find the 21st term of 3, 9, 15, ...  Sequence parameters: first term a = 3; common difference d = 6. Compute t(21) using the AP formula. Choose the correct value.

Accepted Answer

Given a = 3, d = 6, n = 21 Formula t(n) = a + (n−1)d Step-by-step calculation t(21) = 3 + 20×6 = 3 + 120 = 123 Verification Terms grow: 3, 9, 15, ... adding 6 each time; 21st fits 123.

Question 13

Number series (fill the blank): Alternating +5 and −2 pattern.  Given sequence: 28, 33, 31, 36, ?, 39 Identify the missing number following the alternating differences. Choose the correct value.

Accepted Answer

Observation Differences alternate: +5, −2, +5, −2, ... Step-by-step calculation 28 → 33: +533 → 31: −231 → 36: +536 → ? : −2 ⇒ ? = 3434 → 39: +5 (checks)

Question 14

Number series (next square of consecutive odd integers): Continue the pattern.  Given sequence: 1, 9, 25, 49, 81, ? Identify the next term as a perfect square of an odd number. Choose the correct value.

Accepted Answer

Pattern Squares of odd numbers: 1², 3², 5², 7², 9², ... Next term 11² = 121 Common pitfalls Mistaking for arithmetic series; it is a sequence of perfect squares.

Question 15

Number series (identify the missing square): Odd-number squares sequence.  Given sequence: 1, 9, 25, 49, ?, 121 Fill the missing perfect square of an odd integer. Choose the correct value.

Accepted Answer

Observation Sequence = 1², 3², 5², 7², 9², 11², ... Missing term After 7² = 49, the next is 9² = 81, then 11² = 121.

Question 16

Number series (next term): Increasing differences follow n² − 1.  Given sequence: 2, 2, 5, 13, 28, ? Use the difference pattern Δ = 1²−1, 2²−1, 3²−1, 4²−1, ... Choose the correct value.

Accepted Answer

Compute differences 2 → 2: +0 = 1² − 12 → 5: +3 = 2² − 15 → 13: +8 = 3² − 113 → 28: +15 = 4² − 1Next difference = 5² − 1 = 24 Step-by-step calculation Missing term = 28 + 24 = 52 Verification Pattern of differences 0, 3, 8, 15, 24 matches n²−1 with n = 1, 2, 3, 4, 5.

Question 17

Number series (mixed repeated-difference pattern): find the missing term to complete the sequence.  Sequence: 0, 2, 8, 14, ?, 34  Choose the correct value that fits the pattern.

Accepted Answer

Given data Sequence: 0, 2, 8, 14, ?, 34 Concept/Approach Look at first differences and check for a repeating or growing pattern. Step-by-step differences 2 − 0 = 2 8 − 2 = 6 14 − 8 = 6 ? − 14 = d4 34 − ? = d5 Pattern observation After the initial 2, the equal differences appear in pairs that increase by 4: (6, 6), then (10, 10), … Compute the missing terms d4 = 10 ⇒ ? = 14 + 10 = 24 d5 = 10 ⇒ 24 + 10 = 34 (matches) Final Answer 24

Question 18

Number series (add consecutive squares): find the next term.  Sequence: 1, 5, 14, 30, 55, 91, ?  Choose the correct next value.

Accepted Answer

Given data 1, 5, 14, 30, 55, 91, ? Concept/Approach Examine first differences for a recognizable pattern. Step-by-step 5 − 1 = 4 = 2² 14 − 5 = 9 = 3² 30 − 14 = 16 = 4² 55 − 30 = 25 = 5² 91 − 55 = 36 = 6² Next difference = 7² = 49 ⇒ 91 + 49 = 140

Question 19

Arithmetic progression check: determine which option belongs to the series.  Series: 10, 17, 24, 31, 38, … (constant difference)  Choose the number that appears in this series.

Accepted Answer

Concept/Approach The sequence is an arithmetic progression (AP) with common difference d = 7. General term Tn = 10 + (n − 1)·7. Check options (a) 48: (48 − 10)/7 = 38/7 (not integer) (b) 346: (346 − 10)/7 = 336/7 = 48 (integer) ⇒ in AP (c) 574: (574 − 10)/7 = 564/7 (not integer) (d) 1003: (1003 − 10)/7 = 993/7 (not integer) Final Answer 346

Question 20

Division-by-successive-integers pattern: identify the missing second term.  Sequence: 240, ?, 120, 40, 10, 2  Assume successive divisions by 1, 2, 3, 4, and 5. Choose the correct missing value.

Accepted Answer

Concept/Approach Each step divides by the next integer: ÷1, ÷2, ÷3, ÷4, ÷5. Apply 240 ÷ 1 = 240 (2nd term) 240 ÷ 2 = 120 120 ÷ 3 = 40 40 ÷ 4 = 10 10 ÷ 5 = 2

Series Completion Questions