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If a_6=-128, and r=2, what is a_1?​

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

Using the geometric sequence formula:

  • [tex]\rm{A_n=A_1r^{n-1}}[/tex]

[tex] \\ [/tex]

Given that:

  • [tex]A_6 = -128[/tex]
  • r = 2

[tex] \\ [/tex]

Solving ,

  • [tex]\rm{A_n=A_1r^{n-1}}[/tex]

  • [tex]\rm{A_6=A_1(2)^{6-1}}[/tex]

  • [tex]\rm{-128=A_1(2)^{5}}[/tex]

  • [tex]\rm{-128=A_1(32)}[/tex]

  • [tex]\rm{\frac{-128}{32}=\frac{A_1(32)}{32}}[/tex]

  • [tex]\rm{\frac{-128}{32}=\frac{A_1(\cancel{32})}{\cancel{32}}}[/tex]

  • [tex]\rm{-4=A_1}[/tex]

Therefore , [tex]A_1[/tex] is -4

[tex] \\ [/tex]

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

  • [tex]A_1[/tex] is -4

[tex] \\ [/tex]

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