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

Identify Pattern: Identify the pattern in the sequence: 1, _____, 25, 125, 625. We notice that each number seems to be a power of a certain base number.Determine Base Number: Determine the base number and the pattern of exponents. The numbers 1, 25, 125, and 625 are all powers of 5: 5^0, 5^2, 5^3, and 5^4 respectively.Find Missing Term: Find the missing term in the sequence. Since the sequence is increasing and we have 5^0 and 5^2, the missing term should be 5^1. Calculate 5^1 to find the missing number. 5^1 = 5Verify Pattern: Verify the pattern with the calculated missing number. The sequence now reads: 1 (5^0), 5 (5^1), 25 (5^2), 125 (5^3), 625 (5^4). This confirms the pattern of consecutive powers of 5.

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

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Algebra 2

Sequences: mixed review

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Q. Type the missing number in this sequence:

\newline

1

, _____,

25

125

625

Identify Pattern: Identify the pattern in the sequence: $1$ , $\_$ , $25$ , $125$ , $625$ . We notice that each number seems to be a power of a certain base number.
Determine Base Number: Determine the base number and the pattern of exponents. $\newline$ The numbers $1$ , $25$ , $125$ , and $625$ are all powers of $5$ : $5^0$ , $5^2$ , $5^3$ , and $5^4$ respectively.
Find Missing Term: Find the missing term in the sequence. $\newline$ Since the sequence is increasing and we have $5^0$ and $5^2$ , the missing term should be $5^1$ . $\newline$ Calculate $5^1$ to find the missing number. $\newline$ $5^1 = 5$
Verify Pattern: Verify the pattern with the calculated missing number. $\newline$ The sequence now reads: $1$ $(5^0)$ , $5$ $(5^1)$ , $25$ $(5^2)$ , $125$ $(5^3)$ , $625$ $(5^4)$ . $\newline$ This confirms the pattern of consecutive powers of $5$ .