李太太重复书写了“RESILIENCE”这个单词，如图所示。仔细观察下面的字母并回答接下来的问题。

1. Find the number of complete repetitions of the word 'RESILIENCE' in the first 100 letters

The word 'RESILIENCE' has $10$ letters.
Number of repetitions = $100 \div 10 = 10$

2. Calculate the total number of 'E's

There are $3$ 'E's in each word 'RESILIENCE'.
Total number of 'E's = $10 \times 3 = 30$

1. Find the number of complete repetitions of the word 'RESILIENCE' needed to get close to 101 'E's.

Each word has $3$ 'E's.
$101 \div 3 = 33$ with a remainder of $2$.
This means there are $33$ complete words, which contain $33 \times 3 = 99$ 'E's.

2. Calculate the total number of letters up to the 101st 'E'.

The $33$ complete words contain $33 \times 10 = 330$ letters.
The remaining $2$ 'E's must be found in the $34$th word.
In the word 'RESILIENCE', the $2$nd 'E' is at the $7$th position.
Total letters = $330 + 7 = 337$.