1. 5040, 840, 168, 42, 14, ?
Option : A. 7 B. 2 C. 6, D.5
Find the pattern,
Let's divide each term by the next one:
5040 ÷ 840 = 6,
840 ÷ 168 = 5,
168 ÷ 42 = 4,
42 ÷ 14 = 3,
So the pattern is dividing by decreasing numbers: 6, 5, 4, 3...
Continue the pattern,
Next divisor should be 2 (since the pattern decreases by 1 each time).
So,
14 ÷ 2 = 7
Ans: 7
2. 117, 118, 120, 129, 193, ?
Option : A. 210 , B. 420, C. 818, D. 618
Differences:
118−117 = 1 (= 1^1),
120−118 = 2 (= 2^1),
129−120 = 9 (= 3^2),
193−129 = 64 (= 4^3),
Next difference = 5^4 = 625.,
So next term = 193+625=818.,
Ans: 818 (Option C)
3. 2, 3, 7,16, 32, 57, ? Option: A. 93, B. 107, C. 92, D. 100
Find differences,
3 − 2 = 1,
7 − 3 = 4,
16 − 7 = 9,
32 − 16 = 16,
57 − 32 = 25,
Differences = 1, 4, 9, 16, 25 → these are 1², 2², 3², 4², 5²,
Next difference,
Next should be 6² = 36,
Add to last term: 57 + 36 = 93
Ans: 93 (Option A)
4. 6, 7, 11, 20, 36, ? Option A. 60, B. 57, C. 61, D. 51
Find differences,
7 − 6 = 1 ,
11 − 7 = 4 ,
20 − 11 = 9 ,
36 − 20 = 16 ,
Differences = 1, 4, 9, 16 → these are 1², 2², 3², 4² ,
Next difference = 5² = 25,
Add to last term,
36 + 25 = 61
Ans: 61 (Option C)
5. Find known differences: 848, 969, ? , 1282, 1478 Option. A. 1000, B. 1113 C. 1013, D. 999
969 − 848 = 121,
1282 − ? = (unknown) ,
1478 − 1282 = 196 ,
We notice 121 = 11², 196 = 14² → appears like square numbers increasing by 3 in the base (11, 14...).
Continue the pattern , Base numbers: 11, 12, 13, 14 → squares: 121, 144, 169, 196 ,
So the differences should be: +121, +144, +169, +196 ,
Fill in missing term,
848 + 121 = 969,
969 + 144 = 1113,
1113 + 169 = 1282,
1282 + 196 = 1478,
Answer: 1113 (Option B)
6. 1, 4, 9, 16, 25, ? Option. A. 31, B. 36, C. 8, D. 40
1, 4, 9, 16, 25 = 1², 2², 3², 4², 5²
Next = 6² = 36
Ans: 36 (Option B)
7. 32, 57, 93, 142, 206, ? Option. A. 213, B. 26, C. 216, D. 287
Find differences,
57 − 32 = 25,
93 − 57 = 36,
142 − 93 = 49,
206 − 142 = 64,
Differences = 25, 36, 49, 64 → these are 5², 6², 7², 8²,
Next difference,
Next = 9² = 81,
Add to last term,
206 + 81 = 287
Ans: 287 (Option D)