The given sequence is: 5, 20, 80, 320.
To find the pattern, let's look at how each term relates to the previous one:
- \(20 = 5 \times 4\)
- \(80 = 20 \times 4\)
- \(320 = 80 \times 4\)
From this, we can see that each term is obtained by multiplying the previous term by 4.
This indicates that the sequence follows a rule where each term can be expressed as:
- \(a_n = a_{n-1} \times 4\)
We can use this to find the 1st term as:
- \(a_1 = 5\)
- \(a_2 = a_1 \times 4 = 5 \times 4 = 20\)
- \(a_3 = a_2 \times 4 = 20 \times 4 = 80\)
- \(a_4 = a_3 \times 4 = 80 \times 4 = 320\)
Continuing this pattern, we can find the subsequent terms:
- \(a_5 = a_4 \times 4 = 320 \times 4 = 1280\)
- \(a_6 = a_5 \times 4 = 1280 \times 4 = 5120\)
- \(a_7 = a_6 \times 4 = 5120 \times 4 = 20480\)
- \(a_8 = a_7 \times 4 = 20480 \times 4 = 81920\)
Thus, the 8th term of the sequence is 81920.