All the numbers of the below series follow a pattern except for one term of the series. Find the odd one out.
27, 75, 147, 243, 369, 507
Solution
The numbers of the series are following a pattern of $$\left(2k\ +\ 1\right)^2\times\ 3$$
First term of the series is $$=\ \left(2\times1\ +\ 1\right)^2\times\ 3\ =\ 3^2\times\ 3\ =\ 27$$
Second term of the series is $$=\ \left(2\times2\ +\ 1\right)^2\times\ 3\ =\ 5^2\times\ 3\ =\ 75$$
Third term of the series is $$=\ \left(2\times3\ +\ 1\right)^2\times\ 3\ =\ 7^2\times\ 3\ =\ 147$$
Fourth term of the series is $$=\ \left(2\times4\ +\ 1\right)^2\times\ 3\ =\ 9^2\times\ 3\ =\ 243$$
Fifth term of the series is $$=\ \left(2\times5\ +\ 1\right)^2\times\ 3\ =\ 11^2\times\ 3\ =\ 363$$
Sisth term of the series is $$=\ \left(2\times6\ +\ 1\right)^2\times\ 3\ =\ 13^2\times\ 3\ =\ 507$$
So, the odd term of the series is 369, as it should have been 363.
The correct answer is option C.
