<u>Given:</u>
The first term of the sequence is ![a_1=64](https://tex.z-dn.net/?f=a_1%3D64)
The nth term of the sequence is ![a_n=\frac{a_{n-1}}{2}](https://tex.z-dn.net/?f=a_n%3D%5Cfrac%7Ba_%7Bn-1%7D%7D%7B2%7D)
We need to determine the 7th term of the sequence.
<u>Second term:</u>
Substituting n = 2 in the nth term of the sequence, we get;
![a_2=\frac{a_{2-1}}{2}](https://tex.z-dn.net/?f=a_2%3D%5Cfrac%7Ba_%7B2-1%7D%7D%7B2%7D)
![a_2=\frac{a_{1}}{2}](https://tex.z-dn.net/?f=a_2%3D%5Cfrac%7Ba_%7B1%7D%7D%7B2%7D)
![a_2=\frac{64}{2}](https://tex.z-dn.net/?f=a_2%3D%5Cfrac%7B64%7D%7B2%7D)
![a_2=32](https://tex.z-dn.net/?f=a_2%3D32)
Thus, the second term of the sequence is 32.
<u>Third term:</u>
Substituting n = 3 in the nth term of the sequence, we get;
![a_3=\frac{a_{3-1}}{2}](https://tex.z-dn.net/?f=a_3%3D%5Cfrac%7Ba_%7B3-1%7D%7D%7B2%7D)
![a_3=\frac{32}{2}](https://tex.z-dn.net/?f=a_3%3D%5Cfrac%7B32%7D%7B2%7D)
![a_3=16](https://tex.z-dn.net/?f=a_3%3D16)
Thus, the third term of the sequence is 16.
<u>Fourth term:</u>
Substituting n = 4 in the nth term of the sequence, we get;
![a_4=\frac{a_{4-1}}{2}](https://tex.z-dn.net/?f=a_4%3D%5Cfrac%7Ba_%7B4-1%7D%7D%7B2%7D)
![a_4=\frac{16}{2}](https://tex.z-dn.net/?f=a_4%3D%5Cfrac%7B16%7D%7B2%7D)
![a_4=8](https://tex.z-dn.net/?f=a_4%3D8)
Thus, the fourth term of the sequence is 8.
<u>Fifth term:</u>
Substituting n = 5 in the nth term of the sequence, we get;
![a_5=\frac{a_{5-1}}{2}](https://tex.z-dn.net/?f=a_5%3D%5Cfrac%7Ba_%7B5-1%7D%7D%7B2%7D)
![a_5=\frac{8}{2}](https://tex.z-dn.net/?f=a_5%3D%5Cfrac%7B8%7D%7B2%7D)
![a_5=4](https://tex.z-dn.net/?f=a_5%3D4)
Thus, the fifth term of the sequence is 4.
<u>Sixth term:</u>
Substituting n = 6 in the nth term of the sequence, we get;
![a_6=\frac{a_{6-1}}{2}](https://tex.z-dn.net/?f=a_6%3D%5Cfrac%7Ba_%7B6-1%7D%7D%7B2%7D)
![a_6=\frac{4}{2}](https://tex.z-dn.net/?f=a_6%3D%5Cfrac%7B4%7D%7B2%7D)
![a_6=2](https://tex.z-dn.net/?f=a_6%3D2)
Thus, the sixth term of the sequence is 2.
<u>Seventh term:</u>
Substituting n = 7 in the nth term of the sequence, we get;
![a_7=\frac{a_{7-1}}{2}](https://tex.z-dn.net/?f=a_7%3D%5Cfrac%7Ba_%7B7-1%7D%7D%7B2%7D)
![a_7=\frac{2}{2}](https://tex.z-dn.net/?f=a_7%3D%5Cfrac%7B2%7D%7B2%7D)
![a_7=1](https://tex.z-dn.net/?f=a_7%3D1)
Thus, the seventh term of the sequence is 1.