Question

Write a recursive process using sequence notation for the geometric sequence {3,9,27,81,...} that can be used to determine the next term. a1 = 3; an = an − 1 + 3, n > 1 a1 = 3; an = an + 3, n > 1 a1 = 3; an = an − 1 ● 3, n > 1 a1 = 3; an = an − 2 + 3, n > 1

Answer 1

We are given

geometric sequence

3,9,27,81,...

we can see that

first term is 3

so,

$a_1=3$

second term is 9

$a_2=9$

we can also write it as

$a_2=3*3$

we can replace 3 as a1

$a_2=3a_1$

Similarly , we have

third term is 27

$a_3=27$

we can also write it as

$a_3=3*9$

$a_3=3a_2$

so, for nth term

$a_n=3a_n_-_1$ for n>1.........Answer