Question

Write the explicit formula for the geometric sequence represented by the recursive formula. a1 = 11 an = 3 · an-1 A) an = 11 · 3n B) an = 3 · 11n C) an = 11 · 3n-1 D) an = 3 · 11n-1

Answer 1

c. an= 11 * 3n-1. have funnnnn

Answer 2

Option C is correct.

`a_n =11 \cdot 3^(n-1)`

Step-by-step explanation:

Explicit formula for the geometric sequence is given by:

`a_n =a_1 \cdot r^(n-1)`

where r is the common ratio term.

Given the recursive formula for geometric sequence:

`a_1 = 11`

`a_n =3 \cdot a_(n-1)`

For n =2

`a_2 = 3 \cdot a_(2-1)`

`a_2 = 3 \cdot a_1`

⇒
`a_2 = 3 \cdot 11 = 33`

For n =3

`a_3= 3 \cdot a_(3-1)`

`a_3= 3 \cdot a_(2)`

⇒
`a_3= 3 \cdot 33 = 99`

Common ratio(r):

`(a_2)/(a_1) = (33)/(11) = 3`

`(a_3)/(a_2) = (99)/(33) = 3` and so on..

⇒ r = 3

Therefore, the explicit formula for the geometric sequence represented by the recursive formula is:

`a_n =11 \cdot 3^(n-1)`