Question:medium

$ t_1, t_2, t_3, ..., t_n $ are positive integers, $ S_n = t_1 + t_2 + t_3 + ... + t_n $, $ S_1 = 1^2 $, $ S_2 = 3^2 $, $ S_3 = 6^2 $, $ S_4 = 10^2 $, $ S_5 = 15^2 $ and similarly other terms are there. Following this pattern, if $ S_{10} = k^2 $ then $ k = $

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Recognizing common number sequences is a key skill. The sequence 1, 3, 6, 10, 15, ... represents triangular numbers. Knowing the formula $ T_n = n(n+1)/2 $ makes solving such problems much faster.

Updated On: Mar 30, 2026

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The Correct Option is A

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\( t_1, t_2, t_3, ..., t_n \) are positive integers, \( S_n = t_1 + t_2 + t_3 + ... + t_n \), \( S_1 = 1^2 \), \( S_2 = 3^2 \), \( S_3 = 6^2 \), \( S_4 = 10^2 \), \( S_5 = 15^2 \) and similarly other terms are there. Following this pattern, if \( S_{10} = k^2 \) then \( k = \)

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The Correct Option is A

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