Question

In the series AABABCABCDABCDE.. . Which letter occupies the 100th position?

Answer 1

LETTER "I" occupies 100th position

Answer 2

$1^{st}\ position = [\frac{1 \times 2}{2}]^{th}\ position = A = 1^{st}\ letter \\ \\ 3^{rd}\ position = [\frac{2 \times 3}{2}]^{th}\ position = B = 2^{nd}\ letter \\ \\ 6^{th}\ position = [\frac{3 \times 4}{2}]^{th}\ position = C = 3^{rd}\ letter \\ \\ 10^{th}\ position = [\frac{4 \times 5}{2}]^{th}\ position = D = 4^{th}\ letter \\ \\ 15^{th}\ position = [\frac{5 \times 6}{2}]^{th}\ position = E = 5^{th}\ letter$

$\\ \\ \therefore\ [\frac{n(n + 1)}{2}]^{th}\ position = n^{th}\ letter$

$\\ \\ \\ Largest\ triangular\ number\ below\ 100\ \to\ 91 = 13^{th}\ triangular\ number$

$[\frac{13 \times 14}{2}]^{th}\ position = 91^{th}\ position = 13^{th}\ letter = M \\ \\ 92^{th}\ position = 1^{st}\ letter = A \\ \\ (92 + 8)^{th}\ position = (1 + 8)^{th}\ letter \\ \\ = \bold{100^{th}\ position = 9^{th}\ letter = \underline{\underline{I}}}$

$\\ \\ \bold{I}\ is\ the\ answer. \\ \\ \\ Thank\ you.\ Have\ a\ nice\ day. \\ \\ \\ \#adithyasajeevan$