Question

Part 1. Please show work. Please assist me with these math problems. ​

Answer 1

Answer: 1) 2, 3, 4, 9, 32, 279, 8896, 2481705, 22077238784

2) 2,490,924

3) Neither

Explanation:

`S_n=S_(n-2)\cdot (S_(n-1)-1)\quad \\\\S_1=2\quad given\\S_2=3\quad given\\S_3=S_1(S_2-1)\quad =2(3-1)\quad =4\\S_4=S_2(S_3-1)\quad =3(4-1)\quad =9\\S_5=S_3(S_4-1)\quad =4(9-1)\quad =32\\S_6=S_4(S_5-1)\quad =9(32-1)\quad =279\\S_7=S_5(S_6-1)\quad =32(279-1)\quad =8,896\\S_8=S_6(S_7-1)\quad =279(8896-1)\quad =2,481,705\\S_9=S_7(S_8-1)\quad =8896(2481705-1)\quad =22,077,238,784`

`\sum^8_(k=1)S_k\\\\=S_1+S_2+S_3+S_4+S_5+S_6+S_7+S_8\\\\= 2,490,924\\`

Neither

Not arithmetic because the difference between each of the terms is not the same.

S₂ - S₁ S₃ - S₂ S₄ - S₃

3 - 2 = 1 4 - 3 = 1 9 - 4 = 5

Not geometric because the ratios between each of the terms is not the same.

`(S_2)/(S_1)=(S_3)/(S_2)\qquad \rightarrow (3)/(2)=(4)/(3)\qquad \rightarrow \text{cross multiply to get}: 9\\eq 8`