What is the next term of the geometric sequence? (4)/(9),-(4)/(3),4", "

Identify Sequence Type: Identify whether the given sequence is geometric or arithmetic. In the given sequence, each term is obtained by multiplying the previous term by a common ratio. The given sequence is geometric.Find Common Ratio: Identify the common ratio of the sequence. To find the common ratio, divide the second term by the first term. Common Ratio (r) = -(4/3) / (4/9) = -(4/3) * (9/4) = -3Calculate Next Term: Find the next term in the sequence using the common ratio. The third term is 4, so to find the fourth term, multiply the third term by the common ratio. Next Term = 4 * (-3) = -12Check Pattern Consistency: Check the sequence to ensure that the next term follows the pattern. (4/9) * (-3) = -(4/3) -(4/3) * (-3) = 4 4 * (-3) = -12 The pattern is consistent, and the next term is correctly calculated.

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What is the next term of the geometric sequence?

(4)/(9),-(4)/(3),4", "

What is the next term of the geometric sequence? $\newline$ $\frac{4}{9}$ , $-\frac{4}{3}$ , $4$ ,

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

\newline

\frac{4}{9}

-\frac{4}{3}

4

Identify Sequence Type: Identify whether the given sequence is geometric or arithmetic. $\newline$ In the given sequence, each term is obtained by multiplying the previous term by a common ratio. $\newline$ The given sequence is geometric.
Find Common Ratio: Identify the common ratio of the sequence. $\newline$ To find the common ratio, divide the second term by the first term. $\newline$ Common Ratio $r$ = $-\frac{4}{3} \div \frac{4}{9}$ = $-\frac{4}{3} \times \frac{9}{4}$ = $-3$
Calculate Next Term: Find the next term in the sequence using the common ratio. $\newline$ The third term is $4$ , so to find the fourth term, multiply the third term by the common ratio. $\newline$ Next Term = $4 \times (-3) = -12$
Check Pattern Consistency: Check the sequence to ensure that the next term follows the pattern. $\newline$ $(\frac{4}{9}) \cdot (-3) = -(\frac{4}{3})$ $\newline$ $-(\frac{4}{3}) \cdot (-3) = 4$ $\newline$ $4 \cdot (-3) = -12$ $\newline$ The pattern is consistent, and the next term is correctly calculated.