Math  /  Algebra

Question\qquad \qquad - - * \qquad - \qquad \qquad . 4,19,8,24,14,29,19,34,24,39,29,44,4,19,8,24,14,29,19,34,24,39,29,44, \ldots Rule: \qquad \qquad

Studdy Solution

STEP 1

1. The sequence is a list of numbers: 4, 19, 8, 24, 14, 29, 19, 34, 24, 39, 29, 44, ...
2. We need to identify a pattern or rule that describes the sequence.

STEP 2

1. Analyze the sequence to identify any patterns.
2. Determine the rule that generates the sequence.
3. Validate the rule with the given numbers.

STEP 3

Examine the differences between consecutive numbers in the sequence to identify any consistent pattern.
The differences are: 194=15 19 - 4 = 15 819=11 8 - 19 = -11 248=16 24 - 8 = 16 1424=10 14 - 24 = -10 2914=15 29 - 14 = 15 1929=10 19 - 29 = -10 3419=15 34 - 19 = 15 2434=10 24 - 34 = -10 3924=15 39 - 24 = 15 2939=10 29 - 39 = -10 4429=15 44 - 29 = 15

STEP 4

Observe that the differences alternate between +15 +15 and 10 -10 .

STEP 5

The rule for generating the sequence is to alternate between adding 15 and subtracting 10 from the previous number.
The rule for the sequence is: "Start with 4, then alternately add 15 and subtract 10 to generate the next term."

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