How do I find the formula for the sequence: 3, 6, 18, 72, 360, ...?
Answer (3)
a 2 = 2 ⋅ a 1 a 3 = 3 ⋅ a 2 = 3 ⋅ 2 ⋅ a 1 a 4 = 4 ⋅ a 3 = 4 ⋅ 3 ⋅ 2 ⋅ a 1 a 5 = 5 ⋅ a 4 = 5 ⋅ 4 ⋅ 3 ⋅ 2 ⋅ a 1 a n = n ⋅ ( n − 1 ) ⋅ ( n − 2 ) ⋅ ( n − 3 ) ⋅ ... ⋅ 3 ⋅ 2 ⋅ a 1 = n ! ⋅ a 1 a n = 3 ⋅ n !
2x3=6 3x6=18 4x18=72 5x72=360 and so on and so on.......
The formula for the sequence 3, 6, 18, 72, 360 is a_n = 3 × n!. Each term in the sequence is the product of the previous term and an increasing integer, which leads us to a factorial relationship multiplied by 3.
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