Question

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Answer 1

Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -6 and 162, respectively.

an = 2 • 3n - 1

an = 2 • (-3)n - 1

an = 2 • 3n

an = 2 • (-3)n + 1

Answer 2

are those n-1 supposed to be exponents?
example: an= 2 * 3^(n-1)
??

Answer 3

yes

Answer 4

maybe the easiest way is to try to find an for n=2 (that means the 2nd term)

they say a2 is -6
I would look at each choice and ask: do any give the possibility of a negative number?
which choices could give a negative number?

Answer 5

hint: +3 to any power is *always* positive

Answer 6

3^1 means 3 which positive
3^2 is 3*3 still positive
3^3 is 3*3*3 it will always be positive.

So you answer needs a minus sign.... only 2 of the choices have a chance of working..

Answer 7

an = 2 • 3n - 1

an = 2 • (-3)n - 1
either of these @phi

Answer 8

the first one is
\[ a_n = 2\cdot 3^{n-1} \]
isn't it?

the n-1 in the exponent will not make this negative (see my post above)
your 2nd choice is correct. There is one more choice.
Can you find it?

Answer 9

an = 2 • (-3)n + 1

Answer 10

yes

but to avoid confusion you should write your choices as
an = 2 * (-3)^(n+1)

I mean use an up arrow ^ and put parens around the exponent

Let's see if the last choice works? Does it become -6 when n=2

can you figure out what a2 is for
an = 2 * (-3)^(n+1)

Answer 11

in
an = 2 * (-3)^(n+1)

you replace n with 2 everywhere you see it:

a2 = 2* (-3)^(2+1)

can you simplify this?

Answer 12

-54

Answer 13

@phi

Answer 14

is that -6 ? NO.

so let's try the other choice

an= 2* (-3)^(n-1)

what do you get?

Answer 15

you want a2 (replace n with 2 and find the number)

Answer 16

-6!

Answer 17

so that must be the answer. We could check that a5 (replace n with 5) gives us 162, but I am sure it must, because this is the only choice out of the 4 that works for n=2

Answer 18

thank you :)

Answer 19

yw