Question

I have two questions that is messing me up, please help
Which of the following is the formula for the geometric sequence?
900, 300, 100, 33 1/3,...

an = 900(3)n-1
an = 33 1/3 (3)n-1
an = 900(1/3)n-1

Which of the following is the formula for the geometric sequence?
8, -16, 32, -64,...

an = 8(-2)n-1
an = 2(-8)n-1
an = -8(2)n-1

Answer 1

For the first one you need to find the common ratio, like we did in the last question. Then all you need to do is find the first term, which is easy (as it's given to you).

Answer 2

divided 3(first question

Answer 3

So the common ratio is 1/3. What's the first term?

Answer 4

term i think it would be the first number in the line so 900?

Answer 5

Correct. The formula for a geometric sequence is \[\Large a_n = a_1 r^{n-1}\] where r is the common ratio, a1 is the first term. So which formula is correct, with the numbers you found?

Answer 6

the last one?

Answer 7

Yep, an = 900(1/3)n-1 looks right.

Answer 8

The second one can be done in the same way. Find r, and a1.

Answer 9

okay just a sec.

Answer 10

Okay, I need to go, but I can help later if you still need it. But you should be fine, just find r as you did before, divide a term by the term before it, then find a1, and find the formula that matches them.

Answer 11

I cant find the patteren

Answer 12

To find r, divide a term by the term before it: 8, -16, 32, -64

Answer 13

The first term is easy, just the first number in the pattern.

Answer 14

@tcarroll010

Answer 15

-16/8 = r = ??

Answer 16

-2

Answer 17

So that's r. Now find the first term.

Answer 18

first term is 8

Answer 19

the first one??

Answer 20

an = 8(-2)n-1 is correct.

Answer 21

:D thank you so much I understand now so r is the patteren and an is the first term right?

Answer 22

Yep. Well a1 is the first term, an means the nth term. r is the common ratio or multiple from one term to the next.

Answer 23

You're welcome! :D

Answer 24

\[\sqrt{6}(\sqrt{3}+5\sqrt{2})\]

Answer 25

Distribute first:
\[\large \sqrt{6}(\sqrt{3}+5\sqrt{2}) =\sqrt{6}\sqrt{3}+5\sqrt{6}\sqrt{2}) = \]
\[\large \sqrt{6*3}+5\sqrt{6*2} = \sqrt{18}+5\sqrt{12} =\]
\[\large \sqrt{9*2}+5\sqrt{4*3} = \sqrt{9}\sqrt{2}+5\sqrt{4}\sqrt{3} = \]

Try and simplify it now.