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QuestionIdentify the pattern in the numbers 6,18,54,162,4866, 18, 54, 162, 486 and find the next number.

Studdy Solution

STEP 1

Assumptions1. The given sequence of numbers is 6,18,54,162,4866,18,54,162,486 . We are looking for a pattern in this sequence3. We need to use this pattern to predict the next number in the sequence

STEP 2

First, let's observe the given sequence to identify a pattern.6,18,54,162,4866,18,54,162,486

STEP 3

Now, let's look at the ratio between consecutive numbers.186,5418,16254,486162\frac{18}{6}, \frac{54}{18}, \frac{162}{54}, \frac{486}{162}

STEP 4

Calculate the ratios.
186=3,5418=3,16254=3,486162=3\frac{18}{6} =3, \frac{54}{18} =3, \frac{162}{54} =3, \frac{486}{162} =3

STEP 5

From the above calculations, we can see that each number in the sequence is three times the previous number. This is our pattern.

STEP 6

Now that we have identified the pattern, we can use it to find the next number in the sequence. We do this by multiplying the last number in the sequence by3.
Next number=Last number×3Next\, number = Last\, number \times3

STEP 7

Plug in the last number in the sequence into the formula to calculate the next number.
Next number=486×3Next\, number =486 \times3

STEP 8

Calculate the next number.
Next number=486×3=1458Next\, number =486 \times3 =1458The next number in the sequence is1458.

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