The number which best completes the sequence below is: 1, 5, 17, 53, 161, ?

480.

485.
Each term is 2 more than 3 times the one before it.
More explicitly, for n ≥ 0, the n-th term in the sequence is
a_n = 2·3ⁿ – 1.
So
a_0 = 2·3⁰ – 1 = 2·1 – 1 = 1,
a_1 = 2·3¹ – 1 = 2·3 – 1 = 5,
⋮
a_5 = 2·3⁵ – 1 = 2·243 – 1 = 485.

485

the numbers you are adding are:
4, 12, 36, 108, (you keep multiplying the previous number you added by 3)
So the next amount you add is 324
So your answer is 161+324=485

(The number*3)+2 will give you the next number of the sequence.
For example. 1,5,12,53,161,….
(1*3)+2=5
(5*3)+2=17
(17*3)+2=53
(53*3)+2=161
Therefore (161*3)+2 = 485
Hope it helped….

1,5,17,53,161,…
Naturally there is no actual proof.
However after some observation I believe for every number a the next number is 3a+2.
According to this algorithm, the answer is 485.
Of course there is no actual way to prove my answer is correct.
But you can always argue that my answer is right.

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