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The first three terms of a sequence are given. Write your answer as a decimal or whole number. Round to the nearest thousandth (if necessary).

30,120,480,dots
Find the 7 th term.
Answer:

The first three terms of a sequence are given. Write your answer as a decimal or whole number. Round to the nearest thousandth (if necessary). $\newline$ $30,120,480, \ldots$ $\newline$ Find the $7$ th term. $\newline$ Answer:

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Evaluate variable expressions for Sequences

Full solution

Q. The first three terms of a sequence are given. Write your answer as a decimal or whole number. Round to the nearest thousandth (if necessary).

\newline

30,120,480, \ldots

\newline

Find the

7

th term.

\newline

Answer:

Identify Common Ratio: To find the pattern in the sequence, we need to look at the relationship between consecutive terms. $\newline$ We can divide the second term by the first term and the third term by the second term to see if there's a common ratio. $\newline$ Calculation: $120 \div 30 = 4$ and $480 \div 120 = 4$ $\newline$ This shows that each term is $4$ times the previous term, which means the sequence is a geometric sequence with a common ratio of $4$ .
Find $4$ th Term: Now that we know the common ratio is $4$ , we can find the $7$ th term by multiplying the $6$ th term by $4$ . But first, we need to find the $4$ th, $5$ th, and $6$ th terms. The $4$ th term is $480 \times 4$ . Calculation: $480 \times 4 = 1920$
Find $5$ th Term: Next, we find the $5$ th term by multiplying the $4$ th term by $4$ . $\newline$ Calculation: $1920 \times 4 = 7680$
Find $6$ th Term: Now, we find the $6^{th}$ term by multiplying the $5^{th}$ term by $4$ . $\newline$ Calculation: $7680 \times 4 = 30720$
Find $7$ th Term: Finally, we find the $7$ th term by multiplying the $6$ th term by $4$ . $\newline$ Calculation: $30720 \times 4 = 122880$

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