Type the missing number in this sequence: 1, 5, 25, _____, 625, 3,125

Identify Pattern: Identify the pattern in the sequence. The sequence is 1, 5, 25, _____, 625, 3,125. We need to determine if the sequence is arithmetic (each term is added by a constant) or geometric (each term is multiplied by a constant). Looking at the sequence, we can see that each term seems to be a multiple of the previous term, suggesting a geometric sequence.Determine Common Ratio: Determine the common ratio of the geometric sequence. To find the common ratio, we can divide a term by its preceding term. Using the second and first term: 5 / 1 = 5. The common ratio appears to be 5.Verify Ratio: Verify the common ratio with another pair of consecutive terms. Using the last two terms provided: 3,125 / 625 = 5. This confirms that the common ratio is indeed 5.Find Missing Term: Use the common ratio to find the missing term. The term before the missing number is 25. To find the missing term, we multiply 25 by the common ratio of 5. 25 * 5 = 125. The missing number in the sequence should be 125.

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Type the missing number in this sequence: $\newline$ $1$ , $5$ , $25$ , $\_$ , $625$ , $3,125$

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Math Problems

Algebra 2

Find terms of a geometric sequence

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Q. Type the missing number in this sequence:

\newline

1

5

25

\_

625

3,125

Identify Pattern: Identify the pattern in the sequence. $\newline$ The sequence is 1, 5, 25, _____, 625, 3,125. We need to determine if the sequence is arithmetic (each term is added by a constant) or geometric (each term is multiplied by a constant). $\newline$ Looking at the sequence, we can see that each term seems to be a multiple of the previous term, suggesting a geometric sequence.
Determine Common Ratio: Determine the common ratio of the geometric sequence. $\newline$ To find the common ratio, we can divide a term by its preceding term. Using the second and first term: $\frac{5}{1} = 5$ . $\newline$ The common ratio appears to be $5$ .
Verify Ratio: Verify the common ratio with another pair of consecutive terms. $\newline$ Using the last two terms provided: $3,125 / 625 = 5$ . $\newline$ This confirms that the common ratio is indeed $5$ .
Find Missing Term: Use the common ratio to find the missing term. $\newline$ The term before the missing number is $25$ . To find the missing term, we multiply $25$ by the common ratio of $5$ . $\newline$ $25 \times 5 = 125$ . $\newline$ The missing number in the sequence should be $125$ .