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QuestionFind the missing terms in the sequence: 34,3,12,48\frac{3}{4}, 3, 12, 48. Is it arithmetic (A), geometric (G), or neither (N)?

Studdy Solution

STEP 1

Assumptions1. The given sequence is 34,3,12,48\frac{3}{4},3,12,48 . We are to find the missing terms and determine if the sequence is arithmetic (A), geometric (G), or neither ().

STEP 2

First, we need to identify if there are any missing terms in the sequence. In this case, the sequence appears to be complete with no missing terms.
4,,12,48\frac{}{4},,12,48

STEP 3

Next, we need to determine if the sequence is arithmetic. An arithmetic sequence is one in which the difference between any two successive members is constant. We can check this by subtracting the first term from the second term, the second term from the third term, and so on.
3−3,12−3,48−123 - \frac{3}{},12 -3,48 -12

STEP 4

Calculate the differences.
3−34=94,12−3=9,48−12=363 - \frac{3}{4} = \frac{9}{4},12 -3 =9,48 -12 =36

STEP 5

As the differences are not constant, we can conclude that the sequence is not arithmetic.

STEP 6

Next, we need to determine if the sequence is geometric. A geometric sequence is one in which any term divided by its preceding term gives a constant. We can check this by dividing the second term by the first term, the third term by the second term, and so on.
334,123,4812\frac{3}{\frac{3}{4}}, \frac{12}{3}, \frac{48}{12}

STEP 7

Calculate the ratios.
334=4,123=4,4812=4\frac{3}{\frac{3}{4}} =4, \frac{12}{3} =4, \frac{48}{12} =4

STEP 8

As the ratios are constant, we can conclude that the sequence is geometric.
So, the sequence is geometric (G).

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