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)`

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=
`(a_(n))/(a_(n-1))`

Thus, common ratio
`r=(-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.