-9, -8, -4, 5, 21, 46, 82, 131, 195, 276, 376............etc.
Each term can be generated by this formula:a(n) = 1/6 (2n^3 - 3n^2 + n - 54)
4, 9, 25, 49, 121, 169, 289, 361, 529, 841............etc.
Each term can be generated by squaring the next PRIME NUMBER......etc.
+26387 what is the next 2 terms -9 -8 -4 5 21 46
\(\begin{array}{|rcll|} \hline a_n &=& -9 + \underbrace{\frac{(n-1)\cdot n \cdot (n-\frac12 )}{3}}_{\text{sum of the square numbers}} \quad n = 1,2,3, \cdots \\ \hline \end{array}\)
\(\begin{array}{|rcll|} \hline a_7 &=& -9 + \frac{(7-1)\cdot 7 \cdot (7-\frac12 )}{3} \\ a_7 &=& -9 + \frac{6\cdot 7 \cdot (\frac{14}{2}-\frac12 )}{3} \\ a_7 &=& -9 + \frac{6\cdot 7 \cdot (\frac{13}{2})}{3} \\ a_7 &=& -9 + 7 \cdot 13 \\ \mathbf{a_7 }& \mathbf{=} & \mathbf{82} \\\\ a_8 &=& -9 + \frac{(8-1)\cdot 8 \cdot (8-\frac12 )}{3} \\ a_8 &=& -9 + 7\cdot 4 \cdot 5\\ \mathbf{a_8} & \mathbf{=} & \mathbf{131}\\ \hline \end{array}\)
+26387 what is the next 2 terms -9 -8 -4 5 21 46
\(\begin{array}{|rcll|} \hline a_1 &=& -9 \\ a_2 &=& -9 + 1^2 = -8 \\ a_3 &=& -9 + 1^2 + 2^2 = -4 \\ a_4 &=& -9 + 1^2 + 2^2 + 3^2= 5 \\ a_5 &=& -9 + 1^2 + 2^2 + 3^2 + 4^2 = 21 \\ a_6 &=& -9 + 1^2 + 2^2 + 3^2 + 4^2 +5^2 = 46 \\ a_7 &=& -9 + 1^2 + 2^2 + 3^2 + 4^2 +5^2 +6^2 = 82 \\ a_8 &=& -9 + 1^2 + 2^2 + 3^2 + 4^2 +5^2 +6^2 +7^2= 131 \\ \cdots \\ a_n &=& -9 +\underbrace{ (1^2 + 2^2 + 3^2 + 4^2 +5^2 +6^2 +7^2\cdots )}_{\text{sum of the square numbers}} \\ a_n &=& -9 + \underbrace{\frac{(n-1)\cdot n \cdot (n-\frac12 )}{3}}_{\text{sum of the square numbers}} \quad n = 1,2,3, \cdots \\ \hline \end{array} \)
