4 The eleventh term of the sequence 3,-6,12,-24,dots, is (1) -3072 (2) 3072 (3) -6144 (4) 6144

Identify Pattern: Identify the pattern in the sequence. The sequence alternates signs and each term is multiplied by -2 from the previous term. Calculation: -6 = 3 * -2, 12 = -6 * -2, -24 = 12 * -2.General Formula: Determine the general formula for the nth term. Since each term is multiplied by -2, the nth term can be expressed as $ a_n = 3 \times (-2)^{n-1} $. Calculation: $ a_2 = 3 \times (-2)^{2-1} = -6 $, which matches the sequence.Calculate Eleventh Term: Calculate the eleventh term using the formula. Using $ a_n = 3 \times (-2)^{n-1} $, find $ a_{11} = 3 \times (-2)^{11-1} $. Calculation: $ a_{11} = 3 \times (-2)^{10} = 3 \times 1024 = 3072 $.

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The eleventh term of the sequence $\newline$ $3,-6,12,-24,\dots$ , is $\newline$ $(1) -3072$ $\newline$ $(2) 3072$ $\newline$ $(3) -6144$ $\newline$ $(4) 6144$

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Q. The eleventh term of the sequence

\newline

3,-6,12,-24,\dots

, is

\newline

(1) -3072

\newline

(2) 3072

\newline

(3) -6144

\newline

(4) 6144

Identify Pattern: Identify the pattern in the sequence. $\newline$ The sequence alternates signs and each term is multiplied by $-2$ from the previous term. $\newline$ Calculation: $-6 = 3 \times -2$ , $12 = -6 \times -2$ , $-24 = 12 \times -2$ .
General Formula: Determine the general formula for the nth term. $\newline$ Since each term is multiplied by $-2$ , the nth term can be expressed as $a_n = 3 \times (-2)^{n-1}$ . $\newline$ Calculation: $a_2 = 3 \times (-2)^{2-1} = -6$ , which matches the sequence.
Calculate Eleventh Term: Calculate the eleventh term using the formula. $\newline$ Using $a_n = 3 \times (-2)^{n-1}$ , find $a_{11} = 3 \times (-2)^{11-1}$ . $\newline$ Calculation: $a_{11} = 3 \times (-2)^{10} = 3 \times 1024 = 3072$ .