Question

What are the explicit equation and domain for a geometric sequence with a first term of 2 and a second term of −8?

an = 2(−8)n − 1; all integers where n ≥ 1
an = 2(−8)n − 1; all integers where n ≥ 0
an = 2(−4)n − 1; all integers where n ≥ 0
an = 2(−4)n − 1; all integers where n ≥ 1

Answer 1

Hi,
Answer is D.

$a_1=2\\ a_2=-8=a_1*r\Rightarrow\ r= \dfrac{-8}{2} =-4\\ a_2=2*(-4)\\ a_3=2*(-4)^2\\ \boxed{a_n=2*(-4)^{n-1}\ for\ n \geq 1}$

Answer 2

Answer:

The answer is option 4

$a_n=2(-4)^{n-1}$; all integers where n ≥ 1

Step-by-step explanation:

Given the first term and second term of geometric sequence.

we have to find the explicit equation and domain for a geometric sequence.

The formula for nth term of G.P is

$a_n=ar^{n-1}$

$a=2, a_2=-8$

$a_2=ar^{2-1}$

$-8=2r$

$r=-4$

Hence, the explicit equation becomes

$a_n=2(-4)^{n-1}$; all integers where n ≥ 1

Option 4 is correct.