Question

Determine whether the sequence converges or diverges. If it converges, give the limit.

48, 8, four divided by three, two divided by nine, ...

@agent0smith

Answer 1

First: Find the common ratio, by dividing a term by the term before it (use the 2nd and 1st term)

Answer 2

0.16666

Answer 3

So it converges since the common ratio is smaller than 1, now find the sum \[\Large \frac{ a_1 }{ 1-r }\]

Answer 4

Wait confused haha

Answer 5

By...?

Answer 6

IS A1 0.1666

Answer 7

a1 is always first term.

r is common ratio.

Answer 8

47.84

Answer 9

Can't be right... a1 is 48 and r is 1/6, the sum will be greater than 48.

Answer 10

I keep getting 47 >.<

Answer 11

48/(1 - 1/6) =

Answer 12

57.6

Answer 13

Yep :)

Answer 14

But okay what do i do now? Determine whether the sequence converges or diverges. If it converges, give the limit.

Answer 15

We've done everything already.

Answer 16

but these are the aswer choiced :
Converges; two hundred and eighty eight divided by five

Converges; 0

Diverges

Converges; -12432

Answer 17

check this on a calculator:

two hundred and eighty eight divided by five

Answer 18

56.6

Answer 19

288/5 = 57.6 but yep :)

Answer 20

Find an equation for the nth term of the sequence.

-3, -12, -48, -192, ...

Answer 21

Find the common ratio same way as before. First term is easy.

Then plug them in \[\huge a_n = a_1 r^{n-1}\]

Answer 22

4 is the common ratio

Answer 23

Yes and a1 is...?

Answer 24

3?

Answer 25

a1 is just the first term

Answer 26

so -3

Answer 27

an = -3 • 4n - 1

Answer 28

yep, but make sure the (n-1) is the exponent

Answer 29

Find an equation for the nth term of a geometric sequence where the second and fifth terms are -21 and 567, respectively.

Answer 30

Make a new question for this one, it needs more work