Sequences and Series
- The value of x in the sequence 1, 2, 6, 24, x is
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The given sequence is based on the following pattern :
First term = 1
Second term = First term × 2 = 1 × 2 = 2
Third term = Second term × 3 = 2 × 3 = 6
Fourth term = Third term × 4 = 6 × 4 = 24
Fifth term = Fourth term × 5 = 24 × 5 = ?
........... and so on.
Correct Option: D
The given sequence is based on the following pattern :
First term = 1
Second term = First term × 2 = 1 × 2 = 2
Third term = Second term × 3 = 2 × 3 = 6
Fourth term = Third term × 4 = 6 × 4 = 24
Fifth term = Fourth term × 5 = 24 × 5 = ?
∴ ? = 120
Hence, 120 will replace x.
- Which number in the sequence 8, 27, 64,100, 125, 216, 343 is wrongly written?
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In the given sequence all the numbers except 100 are perfect cubes of natural numbers.
As, 8 = 2³,
27 = 3³,
64 = 4³
100 = 10² ≠ 10³
........... and so on.Correct Option: B
In the given sequence all the numbers except 100 are perfect cubes of natural numbers.
As, 8 = 2³,
27 = 3³,
64 = 4³
100 = 10² ≠ 10³
125 = 5³
Hence , the wrong term is 100.
- The next term of the sequence 1, 9, 28, 65, 126, ... is
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The pattern of the sequence is :
1 + 2³ = 1 + 8 = 9
1 + 3³ = 1 + 27 = 28
1 + 4³ = 1 + 64 = 65
1 + 5³ = 1 + 125 = 126
........... and so on.Correct Option: D
The pattern of the sequence is :
1 + 2³ = 1 + 8 = 9
1 + 3³ = 1 + 27 = 28
1 + 4³ = 1 + 64 = 65
1 + 5³ = 1 + 125 = 126
1 + 6³ = 1 + 216 = ?
∴ ? = 217
- The next term of the sequence 2, 3, 6, 7, 14, ..... is
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The pattern of the sequence is :
First term = 2
Second term = First term + 1 = 2 + 1 = 3
Third term = Second term × 2 = 3 × 2 = 6
Fourth term = Third term + 1 = 6 + 1 = 7
Fifth term = Fourth term × 2 = 7 × 2 = 14
Sixth term = Fifth term + 1 = 14 + 1 = ?Correct Option: A
The pattern of the sequence is :
First term = 2
Second term = First term + 1 = 2 + 1 = 3
Third term = Second term × 2 = 3 × 2 = 6
Fourth term = Third term + 1 = 6 + 1 = 7
Fifth term = Fourth term × 2 = 7 × 2 = 14
Sixth term = Fifth term + 1 = 14 + 1 = ?
∴ ? = 15
Hence , The next term of the sequence is 15 .
- The wrong number of the sequence 36, 81, 144, 225, 256, 441 is
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The pattern of the sequence is :
6² = 36
9² = 81
12² = 144
15² = 225
18² = 324 ≠ 256
........... and so on.Correct Option: D
The pattern of the sequence is :
6² = 36
9² = 81
12² = 144
15² = 225
18² = 324 ≠ 256
21² = 441
From above , It is clear that the wrong number of the sequence is 256 .
