Number Series

Step 1: Observe the pattern: 2×1+1=3, 3×2+1=7, 7×3+1=22, 22×7+1=155
Step 2: 155×22+1=3411

Step 1: Observe pattern.
Each term is multiplied by increasing integers and added by same.
Step 2: Check sequence.
145 does not satisfy the pattern.

By observing the pattern of the series, we can see that 414 does not follow the established rule, while the others do. Therefore, 414 is the wrong number.
Thus, the correct answer is (2).

The given puzzle involves multiplying the numbers in a pattern. The first column is multiplied by the second column, and the third column is the sum of those values. The correct result is 888.
Thus, the correct answer is (1).

Step 1: Find the pattern.
The numbers are following a pattern where each term is obtained by multiplying the previous number by a constant and adding a number.
Step 2: Conclusion.
The next number in the series is 65. Final Answer:

Step 1: Center number = product of top numbers + product of bottom numbers.
Step 2: Applying same logic gives missing value = 72.

Step 1: Series of cubes: .

Step 1: First letters increase by +3 positions:
Step 2: Last letters decrease by –2 positions:
Step 3: Numbers follow the pattern: (each term = previous ×2 + 1)

Step 1: Count subscripts of letters D, E, F.
Step 2: Powers increase cyclically: D:1→1→2→2, E:1→2→2→3, F:1→1→2→1
Step 3: Hence next term is D₂E₃F.

Step 1: Observe overlapping pattern: Last two letters of one term become first two of next. QAR → RAS → SAT → TAU
Step 2: Hence next word must start with AU.
Step 3: Only option matching is UAV.

Step 1: Observe alternating pattern of addition.
Step 2: Differences follow: +1, +3, +6, 0, +8, +10, +3.
Step 3: Continuing the pattern gives: 34 + 18 = 52

Step 1: Observe alternating consonant–vowel patterns and alphabetical shifts.
Step 2: Each term follows a fixed letter progression.
Step 3: Option (B) correctly fits the sequence.

Step 1: Observe each letter advances by a fixed number in the alphabet.
Step 2: The missing term must follow the same increment pattern.
Step 3: Option (A) satisfies the progression correctly.

Step 1: Pattern: multiply digits and append sum.
Step 2: Option (b) does not follow the same pattern.

• First letters: G, J, M, P, S (increase by +3) • Last letters: T, R, P, N, L (decrease by −2) • Numbers follow the pattern: 4 → 9 → 20 → 43 → 90

Step 1: Observe the pattern of letters. First letters: Q, R, S, T → increase by one alphabet Next letter = U Second letters: A, A, A, A → constant Next letter = A Third letters: R, S, T, U → increase by one alphabet Next letter = V ⟹ Next term = UAV

Step 1: Observe the subscripts. beginaligned DEF &→ D¹E¹F¹
DEF₂ &→ D¹E¹F²
DE₂F₂ &→ D¹E²F² endaligned
Step 2: The power of letters increases alternately. Next increase is for D: D²E²F³ ⟹ D₂F₃

Step 1: Split the series into two alternating sub-series. Odd-position terms: 3,7,13,21,31 Differences: +4, +6, +8, +10 Even-position terms: 4,7,13,22,34 Differences: +3, +6, +9, +12
Step 2: The next even-position term will increase by +15: 34 + 9 = 43

Step 1: Observe alphabetical progression in each position. Step 2: Letters advance by +3 positions alphabetically from one word to the next. Step 3: Tracing backward from PSVYBE, the previous word must be ADGJM. Thus, the missing term is ADGJM.

Step 1: Observe the pattern: Each word is formed by shifting letters forward in a cyclic alphabetical manner and rearranging positions. Step 2: The missing term must fit symmetrically between EKQWC and IOUAG. Step 3: Only GMNSYE follows the same alphabetical and positional pattern. Hence, the correct answer is GMNSYE.