Answer:
[tex]\frac{1}{2},-\frac{1}{8}, \frac{1}{32}[/tex]
Step-by-step 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;
[tex]T_n=a_1r^n^-^1[/tex]
Therefore;
Second term will be given by;
[tex]T_2=-2(-\frac{1}{4})^2^-^1[/tex]
[tex]T_2=-2(-\frac{1}{4})^1[/tex]
[tex]T_2=\frac{1}{2}[/tex]
Third term will be given by;
[tex]T_3=-2(-\frac{1}{4})^3^-^1[/tex]
[tex]T_3=-2(-\frac{1}{4})^2[/tex]
[tex]T_3=-2(\frac{1}{16})[/tex]
[tex]T_3=1\frac{1}{8}[/tex]
Fourth term will be given by;
[tex]T_4=-2(-\frac{1}{4})^4^-^1[/tex]
[tex]T_4=-2(-\frac{1}{4})^3[/tex]
[tex]T_4=-2(-\frac{1}{64})\\T_4=\frac{1}{32}[/tex]
Thus, the next three terms are; [tex]\frac{1}{2},-\frac{1}{8}, \frac{1}{32}[/tex]
