Question

VEEL

Question

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.

Match each explicit equation with the geometric sequence that it represents

Tiles

an=-3(3)" - 1

an=-3(-3)" - 1

(-3)

= 3(+)***

., = 2436

2, = 243 (1)-1

Pairs

(-3,-9, -27,- 81, -243, ...}

{3, 1.5, 0.75, 0.375, 0.1875, ...}

{-3, 9.-27. 81, -243, ...}

{243, 81, 27, 9, 3, ...}

Answer 1

`a_n=-3(3)^(n-1)` ; {-3,-9, -27,- 81, -243, ...}

`a_n=-3(-3)^(n-1)` ; {-3, 9,-27, 81, -243, ...}

`a_n=3((1)/(2))^(n-1)` ; {3, 1.5, 0.75, 0.375, 0.1875, ...}

`a_n=243((1)/(3))^(n-1)` ; {243, 81, 27, 9, 3, ...}

Explanation:

The first explicit equation is

`a_n=-3(3)^(n-1)`

At n=1,

`a_1=-3(3)^(1-1)=-3`

At n=2,

`a_2=-3(3)^(2-1)=-9`

At n=3,

`a_3=-3(3)^(3-1)=-27`

Therefore, the geometric sequence is {-3,-9, -27,- 81, -243, ...}.

The second explicit equation is

`a_n=-3(-3)^(n-1)`

At n=1,

`a_1=-3(-3)^(1-1)=-3`

At n=2,

`a_2=-3(-3)^(2-1)=9`

At n=3,

`a_3=-3(-3)^(3-1)=-27`

Therefore, the geometric sequence is {-3, 9,-27, 81, -243, ...}.

The third explicit equation is

`a_n=3((1)/(2))^(n-1)`

At n=1,

`a_1=3((1)/(2))^(1-1)=3`

At n=2,

`a_2=3((1)/(2))^(2-1)=1.5`

At n=3,

`a_3=3((1)/(2))^(3-1)=0.75`

Therefore, the geometric sequence is {3, 1.5, 0.75, 0.375, 0.1875, ...}.

The fourth explicit equation is

`a_n=243((1)/(3))^(n-1)`

At n=1,

`a_1=243((1)/(3))^(1-1)=243`

At n=2,

`a_2=243((1)/(3))^(2-1)=81`

At n=3,

`a_3=243((1)/(3))^(3-1)=27`

Therefore, the geometric sequence is {243, 81, 27, 9, 3, ...}.