Question

What are the explicit equation and domain for a geometric sequence with a first term of 3 and a second term of −9?

Answer 1

U can find the common ratio by dividing the 2nd term by the first term
r = -9/3 = -3

an = a1 * r^(n - 1)
a1 = 1st term = 3
r = common difference = -3
now sub
an = 3 * -3^(n - 1) <== ur formula
domain : all integers where n > = 1 <==

Answer 2

Answer: $\ a_{n}=3(-3)^{n-1}$

Step-by-step explanation:

Given: A geometric sequence with its first term $a_1=a=3$

and second term $a_2=-9$

We know that the common ratio in of a geometric sequence=$\frac{a_{n}}{a_{n-1}}$

Thus, common ratio $r=\frac{-9}{3}=-3$

We know that the explicit rule for geometric sequence is written as

$a_{n}=ar^{n-1}\\\Rightarrow\ a_{n}=3(-3)^{n-1}..[\text{by substituting the values of 'a' and 'r' in it }]$

Thus, the explicit rule for the given geometric sequence is $\ a_{n}=3(-3)^{n-1}$ for every n ,a natural number.