Question

Need answer to 4 and 5

Answer 1

Substitute n =1, 2, 3, 4, 5 to get the first five terms.

Explanation:

(4).
`$ g_n  = 2 . 3^(n - 1) $`

To find the first term, substitute n = 1.

Therefore,
`$ g_1 = 2 . 3^(1 - 1) = 2 . 3^(0) = 2 . 1  $` = 2

`$g_2 = 2 . 3^(2 - 1) = 2 . 3 $` = 6

`$ g_3 =  2 . 3^(3 - 1) = 2 . 3^(2) = 2 . 9 $` = 18

`$ g_4 = 2 . 3^(4  - 1) = 2 . 3^(3) = 2 . 27 $` = 54

`$ g_5 =  2 . 3^(5 - 1) = 2 . 3^(4) = 2 . 81 $` = 168

Therefore the first five terms of the sequence are: 2, 6, 18, 54, 168.

(5).
`$ t_n = (2)/(3)t_(n - 1) $`

`$ t_2 = (2)/(3) t_(2 - 1) = (2)/(3)t_1  = (2)/(3)6 $` = 4

`$ t_3 = (2)/(3) t_2 = (2)/(3). 4 = (8)/(3) $`

`$ t_4 = (2)/(3)t_3 = (2)/(3)(8)/(3) = (16)/(9) $`

`$ t_5 = (2)/(3)t_4 = (2)/(3)(16)/(9) = (32)/(27) $`

Therefore the first five terms in the sequence are: 6, 4, 8/3, 16/9, 32/27.