I currently looking what will be the next value to 45 as per given series.

Is there any specific equation available?


closed as off-topic by boboquack, Alconja, Glorfindel, JMP, Rubio Jun 19 '17 at 7:15

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  • 3
    $\begingroup$ Look at the differences between adjacent numbers. Perhaps you can see a pattern. $\endgroup$ – M Oehm Jun 18 '17 at 19:05
  • $\begingroup$ So it means my answer will be 55? Correct? $\endgroup$ – Shyam Shingadiya Jun 18 '17 at 19:08
  • $\begingroup$ You might want to investigate triangular numbers in your spare time. $\endgroup$ – boboquack Jun 18 '17 at 20:20

It's simply the sum of the first n numbers:

$$t_n = \sum_{i = 1}^{n}i = \frac{n\cdot(n+1)}2$$

  • $\begingroup$ And so the next number is 45 + 10 = 55. $\endgroup$ – MikeQ Jun 18 '17 at 19:32
  • $\begingroup$ @MikeQ Yes of course. We can also simply state $t_n = t_{n-1} + n$ with $t_1 = 1$ $\endgroup$ – Paul Evans Jun 18 '17 at 22:53
  • $\begingroup$ Thank you so much @PaulEvans, This is what I looking for. $\endgroup$ – Shyam Shingadiya Jun 19 '17 at 4:46

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