QuestionFind the next two numbers in the sequence: $7, 21, 63, 189$ .

Studdy Solution

STEP 1

Assumptions1. The pattern is a sequence of numbers. . The pattern follows a consistent mathematical rule.

STEP 2

To determine the rule of the sequence, we need to look at the relationship between each consecutive pair of numbers.

STEP 3

By observing, we can see that each number is a multiple of the previous number.

STEP 4

To find the multiplier, divide the second number by the first number, the third number by the second number, and so on.
$Multiplier = \frac{21}{7} =3, \frac{63}{21} =3, \frac{189}{63} =3$

STEP 5

Now that we know the multiplier is3, we can use this to find the next two numbers in the sequence.

STEP 6

Multiply the last given number in the sequence by the multiplier to find the next number.
$Next\, number =189 \\times3$

STEP 7

Calculate the next number.
$Next\, number =189 \\times3 =567$

STEP 8

Repeat the process to find the next number in the sequence.
$Next\, number =567 \\times3$

STEP 9

Calculate the next number.
$Next\, number =567 \\times3 =170$ The next two numbers in the sequence are567 and170.

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