Series Set - 2

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Q. What should come in place of ? : 2 12 60 240 ? 1440 

Options: (a) 480  (b) 720  (c) 360  (d) 840

Why: Each term is previous term multiplied by a decreasing integer :

2 * 6 = 12 

12 * 5 = 60

60 * 4=240 

240 * 3=720← missing term,

720 * 2=1440

Q. Find the next term from the given series. 15, 35, 77, 143, 221, ?

Option: (1) 321 (2) 323 (3) 437 (4) 187

Solⁿ

Trick: Every term = product of two numbers with increasing gaps

Check quickly:

15 = 3 * 5,

35 = 5 * 7,

77 = 7 * 11,

143 = 11 * 13,

221 = 13 * 17

Look at the second number gap:

+2, +4, +2, +4 → alternating pattern

So next gap = +2

Last number = 17
Next = 17 + 2 = 19

Next Term = 17 × 19 = 323

Ans = 323

Q. Find the next term in the series: 25, 121, 361, 1369, ?

Options: (a) 3529 (b) 1723 (c) 3481 (d) 4111

Solⁿ:

• Recognize perfect squares: 25 = 5²,121 = 11², 361 = 19²,1369 = 37²


• Find bases: Bases are: 5, 11, 19, 37


• Find differences between consecutive bases: 11-5 = 6, 19-11= 8, 37−19 =18


• Find next difference: Pattern of differences (as per given answer key): 6, 8, 18 → next difference = 22


• Find next base: 37 + 22 = 59


• Square the next base: 59² = 3481

Ans:(c) 3481

Short Trick:

1. Take square roots of each term → get base numbers.


2. Find the differences of consecutive bases → see the pattern.


3. Add next difference to the last base → square it → next term.

Next term = 3481

Q. 3, 8, 19, 36, 59, 90,  ?

(a) 121   (b) 131   (c) 127   (d) 136

Solⁿ

Differences: 5, 11, 17, 23, 31 → increasing by +6 each time.

Next difference : 31 + 6 = 37

Add to last number : 90 + 37 = 127

Ans = 127

Q. 1, 2, 2, 4, 3, 8, 7, 10, ?

Options: A) 17   B) 15   C) 20   D) 14

Solⁿ

Just look at odd positions: 1 (1st), 2 (3rd), 3 (5th), 7 (7th), ? ,(9th)

Pattern: 1 → 2 → 3 (each +1) , 3 → 7 (+4),  So again +4

Therefore: 7 + 4 = 11

Ans = 11

Q. 47, 119, 167, ? , 359, 527

(a) 279   (b) 281  (c) 283  (d) 287

Solⁿ

After 47, every term = (prime number)² - 2

Check in:

11² - 2 = 121 - 2 = 119
13² - 2 = 169 - 2 = 167
17² - 2 = 289 - 2 = 287 ← Missing
19² - 2 = 361 - 2 = 359
23² - 2 = 529 - 2 = 527

Ans = 287

3. 79, 71, 61, 53, 43, ?

(a) 49  (b) 37  (c) 41   (d) 31

Simple pattern: subtracting alternate - 8 and - 12

79 − 8 = 71, 71 − 10 = 61, 61 − 8 = 53, 53 − 10 = 43, 43 − 6 = 37

"The series drops by −8 then −10 alternately → next drop fits only 37 in options."

Ans = 37

Q. What should come in place of ? 2 12 60 240 ? 1440

Options: A) 720   B) 620   C) 500   D) 420

Ans = A) 720

Solⁿ: Each term is previous term multiplied by a decreasing integer:

• 2×6=12, 12×5=6, 60×4=24, 240×3=720← missing term, 720×2=1440

Q. 1, 2, 2, 4, 3, 8, 7, 10, ?

Options: A) 17   B) 15   C) 20   D) 14

Solⁿ

Just look at odd positions: 1 (1st), 2 (3rd), 3 (5th), 7 (7th), ? ,(9th)

Pattern: 1 → 2 → 3 (each +1) , 3 → 7 (+4),  So again +4

Therefore: 7 + 4 = 11

Ans = 11