Sequences and Series
- Find out the wrong number in the series.
190, 166, 145, 128, 112, 100, 91
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The pattern is :
190 – 24 = 166
166 – 21 = 145
145 – 18 = 127 ≠ 128
........... and so on.Correct Option: D
The pattern is :
190 – 24 = 166
166 – 21 = 145
145 – 18 = 127 ≠ 128
Since , 128 is wrong term . so , 127 is correct term .
127 – 15 = 112
112 – 12 = 100
100 – 9 = 91
Thus , wrong number in the series is 128.
- Find out the wrong number in the sequence : 40960, 10240, 2560, 640, 200, 40, 10
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The pattern is :
40960 ÷ 4 = 10240
10240 ÷ 4 = 2560
2560 ÷ 4 = 640
640 ÷ 4 = 160 ≠ 200Correct Option: B
The pattern is :
40960 ÷ 4 = 10240
10240 ÷ 4 = 2560
2560 ÷ 4 = 640
640 ÷ 4 = 160 ≠ 200
Since , 200 is wrong number . so , 160 is correct number .
160 ÷ 4 = 40
40 ÷ 4 = 10
Thus , required answer is 200.
- The next number of the sequence 3, 5, 9, 17, 33, .... is
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The pattern is :
3 + 2 = 5
5 + 2 × 2 = 5 + 4 = 9
9 + 2 × 4 = 9 + 8 = 17
17 + 2 × 8 = 17 + 16 = 33
33 + 2 × 16 = 33 + 32 = ?Correct Option: A
The pattern is :
3 + 2 = 5
5 + 2 × 2 = 5 + 4 = 9
9 + 2 × 4 = 9 + 8 = 17
17 + 2 × 8 = 17 + 16 = 33
33 + 2 × 16 = 33 + 32 = ?
∴ ? = 65
Thus , The next number of the sequence is 65 .
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The next number of the sequence 1 , 3 , 5 , 7 ,.....is 2 4 8 16
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Sequence of numerators :
⇒ 1, 3, 5, 7, 9 which is odd numbers .
Sequence of denominators :
⇒ 2, 4, 8, 16, 32 which is represents 21 , 22 , 23 , 24 , 25 numbers .Correct Option: D
Sequence of numerators :
⇒ 1, 3, 5, 7, 9 which is odd numbers .
Sequence of denominators :
⇒ 2, 4, 8, 16, 32 which is represents 21 , 22 , 23 , 24 , 25 numbers .∴ Next fraction = 9 32
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When simplified, the sum 1 + 1 + 1 + 1 + 1 +......+ 1 is equal to 2 6 12 20 30 n(n+1)
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Expression = 1 + 1 + 1 + 1 + .......... + 1 2 6 12 20 n(n + 1) = 1 + 1 + 1 + 1 + .......... + 1 1 × 2 2 × 3 3 × 4 4 × 5 n(n + 1) = 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 ......... + 1 - 1 2 2 3 3 4 4 5 n n + 1
Correct Option: D
Expression = 1 + 1 + 1 + 1 + .......... + 1 2 6 12 20 n(n + 1) = 1 + 1 + 1 + 1 + .......... + 1 1 × 2 2 × 3 3 × 4 4 × 5 n(n + 1) = 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 ......... + 1 - 1 2 2 3 3 4 4 5 n n + 1 Expression = 1 - 1 = n + 1 - 1 = n n + 1 n + 1 n + 1