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Predict the next three numbers in the pattern:

[tex]\[5, -20, 80, -320, \square, \square, \square\][/tex]

Sagot :

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].
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