Clearly, the numerators of the fractions in the given sequence follow the series of 2, 3, 5, 7,... and the denominator follows 3, 9, 27, 81, 243, ...
Then, the next term in the given sequence is
.
The given series is 1, 2, 6, 21, 88, ?
1
1 x 1 + 1 = 2
2 x 2 + 2 = 6
6 x 3 + 3 = 21
21 x 4 + 4 = 88
88 x 5 + 5 = 445
Hence, the next number in the given number sequence is 445.
3 x 3 x 3 = 27 - 3 = 24
4 x 4 x 4 = 64 - 4 = 60
5 x 5 x 5 = 125 - 5 = 120
6 x 6 x 6 = 216 - 6 = 210
7 x 7 x 7 = 343 - 7 = 336
Here the letter series is alternative reverse order series. So we get P, N.
There is a gap of four letters between the first and second, the second and third letters.
There is a gap of four letters between the last letter and the first letter of the next term.
The pattern 'mpon' is repeated.
Two series alternate here, with every third number following a different pattern.
In the main series, 4 is added to each number to arrive the next.
In alternate series, 5 is subtracted from each number t arrive the next number.
Here in the main series
3 + 4 = 7
7 + 4 = 11
11 + 4 = 15
15 + 4 = 19
In alternate series
24 - 5 = 19
19 - 5 = 14...
The pattern is *3,+2,*5,+4,*7,+6, . . . . .
So missing term is 623+6=629
The given number series is 1 8 36 ? 1100 7701
It follows a pattern that,
1
1 x 3 + 5 = 8
8 x 4 + 4 = 36
36 x 5 + 3 = 183
183 x 6 + 2 = 1100
1100 x 7 + 1 = 7701
Hence, the missing number in the given series is 183.
The correct pattern is +1, -2, +3, -4, +5, . . . .
So,129 wrong and must be replaced by 123 + 5 = 128
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