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find the fifth mean of geometric sequence where the first term is 7 and the common ratio is 6

please show your solution:)
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AGBOIIIN

[tex]\large{\mathcal{SOLUTION:}}[/tex]

Using the geometric sequence formula

  • [tex]\rm{S_n=A_1r^{n-1}}[/tex]

[tex] \\ [/tex]

Given:

  • n = 5
  • [tex]A_1=7[/tex]
  • r = 6

[tex] \\ [/tex]

Solving ,

  • [tex]\rm{S_n=A_1r^{n-1}}[/tex]

  • [tex]\rm{S_5=7(6)^{5-1}}[/tex]

  • [tex]\rm{S_5=7(6)^{4}}[/tex]

  • [tex]\rm{S_5=7(1296)}[/tex]

  • [tex]\rm{S_5=9072}[/tex]

Therefore, the fifth term is 9072

[tex] \\ [/tex]

[tex]\large{\mathcal{ANSWER:}}[/tex]

  • 9072

[tex] \\ [/tex]

[tex]\boxed{\begin{array}{} \blue{\text{DONT RELY ON CHANCES,}} \\ \red{\text{ WORK FOR THE HARDEST }} \\ \end{array}}[/tex]

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