Question: The 288th term of the series a, b, b, c, c, c, d, d, d, d, e, e, e, e, e, f, f, f, f, f, f... is
Explanation:
In the series a, b, b, c, c, c, d, d, d, d, e, e, e, e, e,...
the first letter of the alphabet is written once, the second is written twice, and the nth letter is written n times.
∴ The number of letters written upto the nth letter is equal to the sum of the first n natural numbers given by, n(n + 1)/2
For n = 23, n(n + 1)/2 = 276 and for n = 24, n(n + 1)/2 = 300
This means the series contains 276 letters in all for the letter corresponding to n = 23 and 300 letters in all for the letter corresponding to n = 24.
∴ The letter corresponding to n = 24 will be the letter occupying the 277th to the 300th place in the series.
But, n = 24 corresponds to letter x.
∴ The 288th letter in the series is x.
Hence, option (d).