Question

260th term of series a,b,b,c,c,c,d,d,d,d,e,e,e,e,e....is?

Answer 1

There are 1 a, 2 b's, 3 c's, 4 d's and so on. Ler the 260 th term be $M$th character.

The number of Mth characters is $M$. The total number of characters till $M$ th character is

$1+2+...+M=\frac{M(M+1)}{2}$. We need

[tex]\frac{M(M+1)}{2} \geq 260\\ M(M+1)\geq 520[/tex]

The least number satisfying the above equation is $M=23$.

Thus the 260th term is the 23rd letter of the alphabet. That is letter 'w".