To find the next three numbers in the sequence [tex]\(5, -20, 80, -320\)[/tex], we need to identify the pattern of the sequence. By examining the sequence:
1. Start with the first number: [tex]\(5\)[/tex]
2. The second number is [tex]\(-20\)[/tex]. It's clear that this number was obtained by multiplying [tex]\(5\)[/tex] by [tex]\(-4\)[/tex]:
[tex]\[
5 \times (-4) = -20
\][/tex]
3. The third number is [tex]\(80\)[/tex]. We notice that [tex]\(-20 \times (-4) = 80\)[/tex]:
[tex]\[
-20 \times (-4) = 80
\][/tex]
4. The fourth number is [tex]\(-320\)[/tex]. Similarly, [tex]\(80\)[/tex] multiplied by [tex]\(-4\)[/tex] gives:
[tex]\[
80 \times (-4) = -320
\][/tex]
From this, we can deduce the pattern: each number is obtained by multiplying the previous number by [tex]\(-4\)[/tex].
Now, let’s determine the next three numbers in the sequence:
1. Start with the last given number in the sequence: [tex]\(-320\)[/tex]
[tex]\[
-320 \times (-4) = 1280
\][/tex]
So, the next number is [tex]\(1280\)[/tex].
2. Multiply [tex]\(1280\)[/tex] by [tex]\(-4\)[/tex]:
[tex]\[
1280 \times (-4) = -5120
\][/tex]
Therefore, the number after [tex]\(1280\)[/tex] is [tex]\(-5120\)[/tex].
3. Multiply [tex]\(-5120\)[/tex] by [tex]\(-4\)[/tex]:
[tex]\[
-5120 \times (-4) = 20480
\][/tex]
Hence, the number after [tex]\(-5120\)[/tex] is [tex]\(20480\)[/tex].
So, the next three numbers in the sequence are [tex]\(1280\)[/tex], [tex]\(-5120\)[/tex], and [tex]\(20480\)[/tex].
