katherineevanet katherineevanet
  • 16-01-2017
  • Mathematics
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Identify the 17th term of a geometric sequence where a1 = 16 and a5 = 150.06. Round the common ratio and 17th term to the nearest hundredth

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LammettHash
LammettHash LammettHash
  • 16-01-2017
[tex]a_5=ra_4=r^2a_3=r^3a_2=r^4a_1\iff150.06=16r^4\implies r\approx\pm1.75[/tex]

Regardless of the sign of the common ratio, then, you will have

[tex]a_{17}=r^{16}a_1\approx16(\pm1.75)^{16}\approx123802.31[/tex]

The actual term would be closer to [tex]123794[/tex] if you didn't have to round.
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