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

Answer:

Option C is correct.

$a_n =11 \cdot 3^{n-1}$

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):

$\frac{a_2}{a_1} = \frac{33}{11} = 3$

$\frac{a_3}{a_2} = \frac{99}{33} = 3$ and so on..

⇒ r = 3

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

$a_n =11 \cdot 3^{n-1}$