One term in the given number series is wrong. Find out the wrong term. $$ 3,10,27,4, 16,64,5,25,125 $$
Step-by-step Solution:
Given series:
3, 10, 27, 4, 16, 64, 5, 25, 125
Observe the series by grouping every third term (i.e. look at the terms in columns if you write them in 3 columns):
Column-1 (positions 1,4,7): 3, 4, 5 — these are consecutive integers.
Column-2 (positions 2,5,8): 10, 16, 25 — these should be squares of 3,4,5, i.e. \(3^2,4^2,5^2 = 9,16,25\).
Column-3 (positions 3,6,9): 27, 64, 125 — these are cubes of 3,4,5, i.e. \(3^3,4^3,5^3\).
So the intended pattern is (reading row-wise):
\(3,\;3^2,\;3^3,\;\;4,\;4^2,\;4^3,\;\;5,\;5^2,\;5^3\)
Comparing with the given series, the second term is 10 but it should be \(3^2=9\).
The wrong term is 10 (should be 9).
Answer: Option (B) 10.