Question

Define a sequence by a1=3 and an=3an−1. Find the first four terms of the sequence. Give a simplified integer answer.

Answer 1

Answer:

The first four terms are 3,9,27,81

Step-by-step explanation:

Step :-1

Given first term of sequence is $a_{1} = 3$

Given 'n' t h term is $a_{n} = 3 a_{n-1}$  .............(1)

here we put  n = 2 in equation (1)

$a_{2} = 3a_{2-1}$

$a_{2} = 3 a_{1}$    ..............2

put $a_{1} = 3$      in equation (2)

$a_{2} = 3(3)$  

$a_{2} = 9$

put n=3 in equation (1)

$a_{3} = 3 a_{3-1}$

$a_{3} = 3a_{2}$

$a_{3} = 3 (9) = 27$

put n= 4 in equation (1)

$a_{4} = 3 a_{4-1}$

$a_{4} = 3 a_{3}$

$a_{4} = 3(27) = 81$

The first four terms of the sequence is

3 , 9, 27 , 81 ....this is geometric sequence

a =3 and ratio term is r =3