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Answer to Question #42506 in Algebra for shasha

Question #42506
Find an equation for the nth term of a geometric sequence where the second and fifth terms are -21 and 567, respectively.

an = 7 • (-3)n + 1

an = 7 • 3n - 1

an = 7 • (-3)n - 1

an = 7 • 3n

help me and show work and explanation pleaase
Expert's answer
The second term equals a2=a1*q=-21, the fifth term equals a5=a1*q^4=567. If we divide the fifth term by the second one, we obtain a5/a2=a1*q^4/(a1*q)=q^3=567/(-21)=-27, so, q^3=-27 and q=-3 correspondingly. Plug into the expression of the second term:  a2=a1*(-3)=-21. Thus, a1=7 and the nth term of the geometric sequence is an=a1*q^(n-1), that is, an=7*(-3)^(n-1).

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