Saylilbaby
  • Saylilbaby
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....
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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Saylilbaby
  • Saylilbaby
@Mehek14
Pawanyadav
  • Pawanyadav
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
Pawanyadav
  • Pawanyadav
Can you solve for a and r.

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zepdrix
  • zepdrix
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! :)
zepdrix
  • zepdrix
And then your 6th term is simply 140 times the r. Solve for r :U do ittttt
Saylilbaby
  • Saylilbaby
i got +-70 @zepdrix
zepdrix
  • zepdrix
70 for the middle term, a_6?
zepdrix
  • zepdrix
Ooo nice job! :)
zepdrix
  • zepdrix
Ya I thought she meant r as well hehe
zepdrix
  • zepdrix
Ya good with the plus/minus. I guess we could have our sequence be alternating.
Saylilbaby
  • Saylilbaby
ok lets do #2 @zepdrix
zepdrix
  • zepdrix
\(\large\rm -2,4,-8,16,...\) Looks like geometric again :) What are we multiplying by each time? Find that r value! :o
Saylilbaby
  • Saylilbaby
by -2 @zepdrix
zepdrix
  • zepdrix
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,\[\large\rm a_n=a_1 r^{n-1}\]
zepdrix
  • zepdrix
\[\large\rm a_{20}=-2(-2)^{19}\]Something like that, ya? :d
Saylilbaby
  • Saylilbaby
i got the answer..... what about the last one @zepdrix
zepdrix
  • zepdrix
\(\large\rm -2,4,10,16....\) 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?
Saylilbaby
  • Saylilbaby
+6 @zepdrix
zepdrix
  • zepdrix
Good :)
zepdrix
  • zepdrix
So to get the 50th term, you'll add that 6 to the first term, 49 times.
zepdrix
  • zepdrix
I mean, 49 of those 6s

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