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

see explanation

Step-by-step explanation:

The n th term of a geometric sequence is

= a

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

= ar² = 12 → (1)

= a = 48 → (2)

Divide (2) by (1)

= = 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

= 3 ← explicit rule

452,489 to the nearest thousand is 452,000