9really nice Q of olympiad level
ans cum out to be
2n - 1 - [(√8n-7 - 1)/2]
where [] is GINT
A sequence of positive integers is constructed as follows: the first term is 1, the following two terms are 2, 4, the following three terms are 5, 7, 9, the following four terms are 10, 12, 14, 16, etc.
Find the n-th term of the sequence.
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3 Answers
9
1wow cele[134][134][134][134][134]
how did u actually think of the ans..... its definitely not trial and error....
cud u explain how u arrived at it.
9lets represent series as
1
24
579
....
.....
........ r th row
now let term n be in r+1 th row
its obviously
2n- 1 -r
now
r(r+1)/2 +1 ≤ n < 1 + (r+1)(r+2)/2 so that n is in r+1 th row
simplifying
√8n-7 - 3 < 2r ≤ √8n-7 - 1
ie in other words r = [(√8n-7 - 1)/2]
