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The first four terms are 3 9 27 81 and 729 is the 6th term.
If the sequence is 1,4,10,19,31,...... Then the sequence formula is, 1 + 3/2n(n - 1) Confirm 5th term....1 + (3/2 x 5 x 4) = 1 + 30 = 31 the 6th (next) term = 1 + (3/2 x 6 x 5) = 1 + 45 = 46
Any number you like.If you fit a linear equation, Un = 24 - 11n then the 6th term is 42.However,Vn = (-29x4 + 290x3 - 1015x2 + 790x + 744)/60 gives the sequence 13, 2, -9, -20, -42.6, and -100Wn = (7x4 - 70x3 + 245x2 - 570x + 648)/20 gives the sequence 13, 2, -9, -20, -22.6, and 0whileXn = (71x4 - 710x3 + 2485x2 - 4210x + 3144)/60 gives the sequence 13, 2, -9, -20, -2.6, and 100By suitable choice of polynomial, any number at all can be in sixth place.
There are infinitely many formulae that generate that sequence for the first 5 terms, but then give different terms for the 6th and onwards. However, the simplest formula (and the one that I guess your teacher is expecting) is based on the fact that there is a fixed common difference of 6 between terms, giving t(n) = 6n - 4 for n = 1, 2, 3, ...
The question seems to be incorrect because, if the definition is 2n + 3 then the third tern should be 9 and the fourth one 11. In that case, t(6) = 2*6 + 3 = 12+3 = 15