Question

Fie sirul infinit de termeni: 1; 3; 6; 10; 15. Al 10-lea termen din sir este egal cu...

P.S.: Trebuie aplicata formula:
$a + (n - 1)d + \frac{1}{2} (n - 1)(n - 2)c$

Answer 1

$1,3,6,10,15...\\ \\ a_1 = 1 \\ a_2 = a_1+2 \\ a_3 = a_2+3\\ a_4 = a_3+4\\...\\a_n=a_{n-1}+n \\ \\ a_1+a_2+a_3+a_4+...+a_n = a_1+a_2+a_3+...+a_{n-1}+1+2+3+...+n\\ \\ a_n =1+2+3+...+n \\ a_n = \dfrac{n(n+1)}{2}\\ \\ \Rightarrow a_{10} = \dfrac{10\cdot 11}{2} = 5\cdot 11 = 55$