What is the next term of the geometric sequence? 2,10,50", "

Identify Sequence Type: Identify whether the given sequence is geometric or arithmetic. In the given sequence, each term after the first is obtained by multiplying the previous term by a constant number, which suggests that the sequence is geometric.Find Common Ratio: Determine the common ratio of the sequence. To find the common ratio, divide the second term by the first term, or the third term by the second term. 10 / 2 = 5 and 50 / 10 = 5 Common Ratio: 5Calculate Next Term: Calculate the next term in the sequence using the common ratio. The last term given in the sequence is 50. To find the next term, multiply the last term by the common ratio. 50 * 5 = 250Verify Result: Verify the result to ensure there are no mathematical errors. The sequence follows a pattern of multiplication by 5. The progression from 2 to 10 (2 * 5), and from 10 to 50 (10 * 5), correctly leads to the next term being 50 * 5, which is 250.

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What is the next term of the geometric sequence?

2,10,50", "

What is the next term of the geometric sequence? $\newline$ $2, 10, 50$ ,

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Q. What is the next term of the geometric sequence?

\newline

2, 10, 50

Identify Sequence Type: Identify whether the given sequence is geometric or arithmetic. $\newline$ In the given sequence, each term after the first is obtained by multiplying the previous term by a constant number, which suggests that the sequence is geometric.
Find Common Ratio: Determine the common ratio of the sequence. $\newline$ To find the common ratio, divide the second term by the first term, or the third term by the second term. $\newline$ $\frac{10}{2} = 5$ and $\frac{50}{10} = 5$ $\newline$ Common Ratio: $5$
Calculate Next Term: Calculate the next term in the sequence using the common ratio. $\newline$ The last term given in the sequence is $50$ . To find the next term, multiply the last term by the common ratio. $\newline$ $50 \times 5 = 250$
Verify Result: Verify the result to ensure there are no mathematical errors. $\newline$ The sequence follows a pattern of multiplication by $5$ . The progression from $2$ to $10$ ( $2 \times 5$ ), and from $10$ to $50$ ( $10 \times 5$ ), correctly leads to the next term being $50 \times 5$ , which is $250$ .