Step 1: Analyzing Patterns:
The series: a (1 time), b (2 times), c (3 times), d (4 times), e (5 times), f (6 times), g (7 times), and so on.
The number of terms up to the letter that appears \(n\) times is:
\[
S_n = \frac{n(n+1)}{2}
\]
Step 2: Finding the Letter:
We need the 288th term. Find \(n\) such that:
\[
S_{n-1} < 288 \leq S_n
\]
\[
S_{23} = \frac{23 \times 24}{2} = 276
\]
\[
S_{24} = \frac{24 \times 25}{2} = 300
\]
Since \(276 < 288 \leq 300\), the 288th term belongs to the block of the 24th letter.
Alphabet: a = 1, b = 2, c = 3, ..., 24th letter = X.