Question

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?

Answer 1

Answer:

$\frac{1}{2},-\frac{1}{8}, \frac{1}{32}$

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;

$T_n=a_1r^n^-^1$

Therefore;

Second term will be given by;

$T_2=-2(-\frac{1}{4})^2^-^1$

$T_2=-2(-\frac{1}{4})^1$

$T_2=\frac{1}{2}$

Third term will be given by;

$T_3=-2(-\frac{1}{4})^3^-^1$

$T_3=-2(-\frac{1}{4})^2$

$T_3=-2(\frac{1}{16})$

$T_3=1\frac{1}{8}$

Fourth term will be given by;

$T_4=-2(-\frac{1}{4})^4^-^1$

$T_4=-2(-\frac{1}{4})^3$

$T_4=-2(-\frac{1}{64})\\T_4=\frac{1}{32}$

Thus, the next three terms are; $\frac{1}{2},-\frac{1}{8}, \frac{1}{32}$