Write a formula/formulae for the following sequence:
b). 1,3,6,10,15,...
I am not getting any pattern here, from which to derive a formula. This sequence does not look like the examples I could solve: like
a) 1,0,1,0,1...
where I got that $S_n =1 $ (for $n=1,3,5,7,...$) and $S_n=0$ (for $n=2,4,6,8,...$)
or
c.) 1,1,1,2,1,3,1,4,1,...
where $S_n=1$ for $n=1,2,3,5,7,...$ and $S_n= n/2$ for $n=4,6,8,.. $
$\endgroup$ 22 Answers
$\begingroup$For (b) you can observe the difference between next and previous terms is in A.P.
Thus you can define it recursively as $s_1 = 1$, $s_{n+1}=s_n + (n+1)$.
$\endgroup$ 1 $\begingroup$Mike Pierce has already given the answer.
Still let me mention that the $n$-th term of the sequence is the sum of the first $n$ natural numbers.
Hence $$s_n = \frac{n(n+1)}{2}$$
It is also possible to derive the above by solving the recurrence relation given by Amey Deshpande.
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