1 2 5 14 41
Since every term is expressed with respect to the immediately preceding term, this is a recursive sequence, where t1 = 1 and tn+1 = 3tn - 1, n = 1, 2, 3, ...
t1 = 1
t2 = 3(1) - 1 = 2
t3 = 3(2) - 1 = 5
t4 = 3(5) - 1 = 14
t5 = 3(15) - 1 = 41
next
t6 = 3(41) - 1 = 122
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41 should be in between 14 and 122
The pattern in the sequence is that each number is obtained by multiplying the previous number by 3 and subtracting 1. 1 x 3 - 1 = 2 2 x 3 - 1 = 5 5 x 3 - 1 = 14 14 x 3 - 1 = 41 41 x 3 - 1 = 122 Therefore, the next number in the sequence would be 122 x 3 - 1 = 365.
The next number in the sequence is 15 - the sequence goes x2, +2, -1
The simplest sequence appears to be 15 1*2=2 2+2=4 4-1=3 3*2=6 6+2=8 8-1=7 7*2=14 14+2=16 16-1=15 Multiply by 2 Add 2 Subtract 1 Repeat
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