Question

The sequence given is defined using a recursion formula. Write the first four terms of the sequence. a 1 equals 3 and a Subscript n Baseline equals 2 a Subscript n minus 1 Baseline plus 5 for n greater than or equals 2

Answer 1

Answer: 3 , 6 , 12 , 24

Explanation:

The given recursive formula :

`a_n=2a_(n-1)` for n ≥ 2 and n be any natural number.

Also, First term is given as
`a_1=3`

Then, for n= 2 , we have

`a_2=2a_(2-1)=2a_1=2(3)=6`

For n= 3 , we have

`a_3=2a_(3-1)=2a_2=2(6)=12`

For n= 4 , we have

`a_4=2a_(4-1)=2a_3=2(12)=24`

The first four terms of sequence =
`a_1 ,\ a_2,\ a_3,\ a_4=3 ,\ 6 ,\ 12 ,\ 24`