91Ó°ÊÓ

We have $a_1=128,r=\frac{1}{4}$.

We know that in a geometric mean, we have the common ration between the terms, same. So by multiplying the ration with the preceding term, we can get the succeeding term. Through this we will find the first five terms with help of first term.

We have the first term as $128$and the ratio as $\frac{1}{4}$.

So to find the second term, multiply the ratio with the first term, i.e.,

$$\begin{gathered} a_2=a_1×r \\ =128×\frac{1}{4} \\ =32 \end{gathered}$$
The second term is$32$.

We will follow the same procedure. So to get the third term, we will multiply the ratio with the second term, i.e.,

$$\begin{gathered} a_3=a_2×r \\ =32×\frac{1}{4} \\ =8 \end{gathered}$$
The third term is$8$.

To find fourth term, multiply the ratio with the third term, i.e.,

$$\begin{gathered} a_4=a_3×r \\ =8×\frac{1}{4} \\ =2 \end{gathered}$$
The fourth term is$2$.

To find fifth term, multiply the ratio with the fourth, i.e.,
$$\begin{gathered} a_5=a_4×r \\ =2×\frac{1}{4} \\ =\frac{1}{2} \end{gathered}$$
The fifth term is$\frac{1}{2}$.