Answer to Question #110491 in Algebra for Jehan

Question

After being told a student started to write like this: aAabBbcCcdDdeEe…………zZzaAabBb….. That means, at first a small letter then a capital letter then again a small letter. After finishing at ‘z’ he will start again from ‘a’. What will be the 2019th letter? Is it a capital or small letter?

Answer 1

From the general sequence we can say:

1. every letter uses 3 times
2. every new letter begins with a small, then capital and again a small letter

English alphabet has 26 letters. We can find how many letters will there be during writing from a to z letter. The unique sequence has 26*3 = 78 letters.

Now let's find out how many times student will write that unique sequence:

2019/78 = 25.88 times

.88 shows us that our letter will be at the very end of unique sequence. So we just need to find what's the number of the last letter in 26th unique sequence:

78*26 = 2028

Now let's find out how many letters we should minus from the end of our unique sequence:

2028 - 2019 = 9

9 letters from the end look like: zZzyYyxXx

69th letter(78-9) of our unique sequence and also 2019th of our general sequence will be: small w