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 first letter moves 3 steps forward. The second and third letters move 2 steps forward.
The given sequence is a combination of two series:
i.)Y,T, O and ii.)B, G, ?
i. consists of 2nd, 7th, 12th letters from end of English alphabet,while
ii. consists of 2nd, 7th, 12th letters from beginning of English alphabet
So, the missing letter in ii.) is the 12th letter from the beginning of English alphabet,which is L.
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 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
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