Question

If the alphabets are written in the sequence of a, bb, ccc, dddd, eeeee, ffffff, . What will be the 120th letter?

Answer 1

Answer:

O will be the 120th Letter

Step-by-step explanation:

If the alphabets are written in the sequence of a, bb, ccc, dddd, eeeee, ffffff, . What will be the 120th letter

1st Letter  -  1st Alphabet

2nd & 3rd Letter - 2nd Alphabet

4th , 5th & 6th Letter - 3rd Alphabet

7th , 8th ,9th & 10th Letter  - 4th Alphabet

and so on

1st letter of nth Alphabet  = Last lette of (n-1)th Alphabet + 1

Last letter of nth Alphabet = Last Letter of nth Alphabet

Last Letter of nth Alphabet = Sum of n Alphabets

= n(n+1)/2

1st letter of n-1 th Alphabet  = (n-1)n/2

1st Letter of nth Alphabets = (n-1)n/2 + 1

(n-1)n/2 + 1 , ............... n(n+1)/2

120 Should be any one of these

n(n+1)/2 ≥ 120 ≥  (n-1)n/2

Solving first

n(n+1)/2 ≥ 120

=> n² + n ≥ 240

=> n² + n - 240  ≤ 0

n ≥ 15

(n-1)n/2 < 120

n² - n < 240

n² - n - 240 < 0

=>  n < 16

From Both n = 15

=> 120th Letter will have 15th Alphabet

O is the 15th Alphabet

O will be from 106 to 120 Letters

120th letter is O