Question

Given that a3 = 12 and a5 = 48, find the explicit rule for the geometric sequence, given that the common ratio is positive

Answer 1

Answer:

hello : q=2

Step-by-step explanation:

look this solution :

Answer 2

Answer:

see explanation

Step-by-step explanation:

The n th term of a geometric sequence is

$a_{n}$ = a$r^{n-1}$

where a is the first term and r the common ratio, thus

$a_{3}$ = ar² = 12 → (1)

$a_{5}$ = a$r^{4}$ = 48 → (2)

Divide (2) by (1)

$\frac{ar^4}{ar^2}$ = $\frac{48}{12}$ = 4

r² = 4 ⇒ r = ± 2 ⇒ r = 2 ← since r > 0

Substitute r = 2 into (1) for corresponding value of a

4a = 12 ⇒ a = 3

Hence

$a_{n}$ = 3$(2)^{n-1}$ ← explicit rule