Q.347. nth term of a series

Question 347.
What is the nth term of 0,  2,   5,   9,  14,  .... ?

Answer 347.
It can be observed that tn - t(n-1) = n
=>
t2 - t1 = 2
t3 - t2 = 3
t4 - t3 = 4
.....
......
tn - t(n-1) = n
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Adding,
tn - t1 = 2 + 3 + 4 + ... + n
=> tn - 0 = n(n+1)/2 - 1
=> tn = (1/2) (n^2 + n - 2).

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