Question

the 5th term in a geometric sequence is 140. the 7th term is 35. what are the possible values of the 6th term of the sequence?
what is the 20th term of the sequence that begins -2,4,-8,16..?
what is the 50th term of the sequence that begins -2,4,10,16....

Answer 1

@Mehek14

Answer 2

It is geometric progression so it should be like this
First term =a
Second term=ar
Third termterm=ar^2
.
.
.

5th term=ar^4=140
.
.7th term=ar^6=35

Solve above two equation and find a,r

Answer 3

Can you solve for a and r.

Answer 4

Geometric means you're `multiplying` by some `common ratio` to get from one term to the next.

So to get from term 5 to term 6, you multiply by r.
\(\large\rm a_5=140\)
\(\large\rm a_6=140r\)
a_6 is just the previous term multiplied by this r value.
Then to get from term 6 to term 7, you multiply by r again,
\(\large\rm a_7=140r\cdot r\)
\(\large\rm a_7=140r^2\)
And then told us the value of a_7, so let's plug that in,\[\large\rm 35=140r^2\]Solve for r! :)

Answer 5

And then your 6th term is simply 140 times the r.
Solve for r :U do ittttt

Answer 6

i got +-70 @zepdrix

Answer 7

70 for the middle term, a_6?

Answer 8

Ooo nice job! :)

Answer 9

Ya I thought she meant r as well hehe

Answer 10

Ya good with the plus/minus.
I guess we could have our sequence be alternating.

Answer 11

ok lets do #2 @zepdrix

Answer 12

\(\large\rm -2,4,-8,16,...\)
Looks like geometric again :)
What are we multiplying by each time?
Find that r value! :o

Answer 13

by -2 @zepdrix

Answer 14

Good.
And how do you get from the 1st to the 20th term?
I guess you would multiply the first term by r ... 19 times!
(One less because we didn't apply r to get our first term a_1)

Or if you prefer, you can just lean on your formula that they taught you,\[\large\rm a_n=a_1 r^{n-1}\]

Answer 15

\[\large\rm a_{20}=-2(-2)^{19}\]Something like that, ya? :d

Answer 16

i got the answer..... what about the last one @zepdrix

Answer 17

\(\large\rm -2,4,10,16....\)

The last one was pretty obvious, we were doubling each time,
so it was multiplication by 2.

How bout this one?
Geometric or Arithmetic?
Multiplying or Adding something each term?

Answer 18

+6 @zepdrix

Answer 19

Good :)

Answer 20

So to get the 50th term,
you'll add that 6 to the first term, 49 times.

Answer 21

I mean, 49 of those 6s