Question

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

Answer 1

Answer:

The fifth term of the sequence is 325.

Step-by-step 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  

•                       $t_2=3(t_2_-_1)-2$

                               $t_2=3(t_1)-2$

                               $t_2=3\times 5-2$  

                               $t_2=15-2 = 13$

• Similarly,  $t_3=3(t_3_-_1)-2$

                        $t_3=3(t_2)-2$

                        $t_3=3\times 13-2$  

                        $t_3=39-2 = 37$  

   

•  $t_4=3(t_4_-_1)-2$

          $t_4=3(t_3)-2$

          $t_4=3\times 37-2$  

          $t_4=111-2 = 109$  

•  $t_5=3(t_5_-_1)-2$

          $t_5=3(t_4)-2$

          $t_5=3\times 109-2$  

          $t_5=327-2 = 325$  

Therefore, the fifth term of the sequence is 325.