The letter series below is written in groups that grow by one letter each time: P, then P Q, then P Q R, and so on.
P P Q P Q R P Q R S P Q R S T ...
If the series is continued in the same way, which letter will be the 40th letter?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → S
The 1st group has 1 letter, the 2nd has 2 letters, and so on, so the first k groups together have \(1+2+\dots+k\) letters. Find the group in which the 40th letter falls.
Letters in the first 8 groups \(=1+2+3+4+5+6+7+8=36\)
Letters in the first 9 groups \(=36+9=45\), which is more than 40
So the 40th letter is in the 9th group, P Q R S T U V W X, at place \(40-36=4\)
The 4th letter of that group is S