$$ 3,6,12,24, \ldots,\left(8^{ ext {th }} ight. $$ term $$ ) $$

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$$ 3,6,12,24, \ldots,\left(8^{	ext {th }}ight. $$ term $$ ) $$

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The 8th term of the sequence is 384. The sequence given is $$ 3, 6, 12, 24, \ldots $$. To find the pattern, let's look at the ratios of consecutive terms: - $$ \frac{6}{3} = 2 $$ - $$ \frac{12}{6} = 2 $$ - $$ \frac{24}{12} = 2 $$ It appears that each term is multiplied by 2 to get the next term. We can express the $$ n $$-th term of the sequence as follows: - The first term $$ a_1 = 3 $$ - The second term $$ a_2 = 3 \times 2 = 6 $$ - The third term $$ a_3 = 3 \times 2^2 = 12 $$ - The fourth term $$ a_4 = 3 \times 2^3 = 24 $$ In general, the $$ n $$-th term can be expressed as: $$ a_n = 3 \times 2^{n-1} $$ Now, to find the 8th term $$ a_8 $$: $$ a_8 = 3 \times 2^{8-1} = 3 \times 2^7 = 3 \times 128 = 384 $$ Thus, the 8th term of the sequence is $$ \boxed{384} $$.

\( 3,6,12,24, \ldots,\left(8^{\text {th }}\right. \) term \( ) \)

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\( 3,6,12,24, \ldots,\left(8^{\text {th }}\right. \) term \( ) \)

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