Which one of the following is the wrong number in the series 6, 14, 30

Let’s examine the relationship between consecutive terms.
T(2) = 14. Is there a relation to T(1)=6? 6 * 2 + 2 = 12 + 2 = 14.
Let’s test this pattern for the next term: T(n+1) = 2 * T(n) + 2.
T(3) = 2 * T(2) + 2 = 2 * 14 + 2 = 28 + 2 = 30. This matches the given T(3).
Now let’s test this pattern for the fourth term:
Expected T(4) = 2 * T(3) + 2 = 2 * 30 + 2 = 60 + 2 = 62.
However, the given fourth term is 64. This indicates that 64 might be the wrong number.

Let’s assume the expected T(4) (which is 62) was correct and test the pattern for the fifth term:
Expected T(5) = 2 * (Expected T(4)) + 2 = 2 * 62 + 2 = 124 + 2 = 126.
This matches the given T(5).

So, the pattern T(n+1) = 2 * T(n) + 2 holds for all terms except for the fourth term, which should be 62 according to the pattern, but is given as 64. Therefore, 64 is the wrong number in the series.