Question

The missing number in the series 1, 4, 27,____, 3125 is: 81 35 729 256 115

Normal distributions
ANSWERED
asked 2021-06-15
The missing number in the series 1, 4, 27,____, 3125 is: 81 35 729 256 115

Answers (1)

2021-06-16

Given series:
1,4,27,?,3125
We note that 4 is the square of 2, while 27 is the third power of 27 and 3125 is the fifth power of 5:
\(\displaystyle{1}^{{1}},{2}^{{2}},{3}^{{3}},?,{5}^{{5}}\)
Thus we note that the nth term in the sequence appears to be the nth power of n. That is, \(a_{n} = n^n\) when an represents the nth term in the sequence.
This then implies that we expect the fourth term in the sequence to be \(\displaystyle{4}^{{4}}\).
\(\displaystyle{a}{4}={4}^{{4}}={256}\)

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