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The first term of a geometric sequence is -2 and the common ratio is -1/4. what are the next three terms of the sequence?

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The first term of a geometric sequence is -2 and the common ratio is -1/4. what are-example-1
User SOA Nerd
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Answer:


(1)/(2),-(1)/(8), (1)/(32)

Explanation:

From the question;

  • The first term of a geometric sequence, a₁ is -2
  • The common ratio, r is -1/4

We are required to determine the next three terms of the sequence;

We need to know that;

nth term is a geometric sequence is given by;


T_n=a_1r^n^-^1

Therefore;

Second term will be given by;


T_2=-2(-(1)/(4))^2^-^1


T_2=-2(-(1)/(4))^1


T_2=(1)/(2)

Third term will be given by;


T_3=-2(-(1)/(4))^3^-^1


T_3=-2(-(1)/(4))^2


T_3=-2((1)/(16))


T_3=1(1)/(8)

Fourth term will be given by;


T_4=-2(-(1)/(4))^4^-^1


T_4=-2(-(1)/(4))^3


T_4=-2(-(1)/(64))\\T_4=(1)/(32)

Thus, the next three terms are;
(1)/(2),-(1)/(8), (1)/(32)

User Erwin Alberto
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