Find the missing number:

2, 12, 36, 80, __, 222

150
(Pattern: ×1+10, ×2+12, ×3+14, ×4+16 → 80×4+16 = 150)

Find the wrong number in the series:

3, 7, 15, 31, 63, 127, 255

255
(Pattern: ×2+1 → 3×2+1=7, 7×2+1=15, 15×2+1=31, 31×2+1=63, 63×2+1=127, 127×2+1=255 (incorrect, should be 255))

Riddle:

I am a two-digit prime number.

If you subtract my reverse, you get 36.

Who am I?

73
(73 - 37 = 36; Both 73 and 37 are prime numbers)

True or False:

The sequence 1, 3, 9, 27, 81, 243 follows an arithmetic progression.

False
(It follows a geometric progression with a common ratio of ×3.)

Find the missing number:

121, 100, 81, __, 49, 36

64
(Pattern: squares of descending numbers → 11², 10², 9², 8², 7², 6²)

Statement-Based Question:

Statement: The number 153 belongs to a special number series.

Which category does it belong to?

Armstrong Numbers
(153 = 1³ + 5³ + 3³)

Find the wrong number in the series:

500, 450, 400, 340, 290, 240

340
(Pattern: -50, -50, -60, -50, -50 → 400-50=350, not 340)

Find the missing number:

3, 14, 39, 84, __, 224

155
(Pattern: (n² + n) → 3=(1²+2), 14=(3²+5), 39=(5²+6), 84=(7²+7), 155=(9²+8), 224=(11²+9))

True or False:

The series 4, 9, 25, 49, 81 follows the Fibonacci sequence.

False
(It is a series of squares of prime numbers → 2², 3², 5², 7², 9² (wrong, correct would be 11²=121))

Find the missing number:

1, 2, 6, 24, __, 720

120
(Factorial series: 1!, 2!, 3!, 4!, 5!, 6! → 5! = 120)

Fill in the blank:

A geometric progression has a first term of 5 and a common ratio of 4. The 5th term is ___.

1280
(5 × 4⁴ = 5 × 256 = 1280)

Case Study:

A factory produces widgets following this pattern:

10, 20, 40, 80, __, 320

If the trend continues, how many widgets will be produced in the 6th cycle?

160
(Pattern: ×2 → 10×2=20, 20×2=40, 40×2=80, 80×2=160, 160×2=320)

Find the wrong number:

2, 10, 30, 68, 130, 222

68
(Pattern: n²+2 → 1²+2=3, 2²+2=6, 3²+2=11, 4²+2=18, 5²+2=27, 6²+2=38 → 68 is incorrect, should be 38)

Riddle:

I am a perfect cube and the sum of my digits is 10.

Who am I?

512
(512 = 8³ and 5+1+2=10)

Find the missing number:

13, 29, 61, __, 253

125
(Pattern: 13×2+3=29, 29×2+3=61, 61×2+3=125, 125×2+3=253)