Question

Find the fifth term of the sequence given by the recursive formula
ty = 5 and tn = 3tn-1 - 2

Answer 1

The fifth term of the sequence is 325.

Explanation:

We are given the following recursive formula ;

`t_1` = 5 and
`t_n=3(t_n_-_1)-2`

Now, we have to find the fifth term of the given sequence, i.e;

• 
  `t_1` = 5

• 
  `t_2=3(t_2_-_1)-2`

`t_2=3(t_1)-2`

`t_2=3* 5-2`

`t_2=15-2 = 13`

• Similarly,
  `t_3=3(t_3_-_1)-2`

`t_3=3(t_2)-2`

`t_3=3* 13-2`

`t_3=39-2 = 37`

• 
  `t_4=3(t_4_-_1)-2`

`t_4=3(t_3)-2`

`t_4=3* 37-2`

`t_4=111-2 = 109`

• 
  `t_5=3(t_5_-_1)-2`

`t_5=3(t_4)-2`

`t_5=3* 109-2`

`t_5=327-2 = 325`

Therefore, the fifth term of the sequence is 325.