Find the 8th term of the geometric sequence shown below. 7x^(4),28x^(6),112x^(8),dots Answer:

Identify common ratio: Identify the common ratio (r) of the geometric sequence by dividing the second term by the first term. Calculation: $ r = \frac{28x^6}{7x^4} $Calculate common ratio: Simplify the expression to find the common ratio. Calculation: $ r = 4x^2 $Use nth term formula: Use the formula for the nth term of a geometric sequence, which is $ a_n = a_1 \cdot r^{(n-1)} $, where $ a_1 $ is the first term and $ n $ is the term number. Calculation: The 8th term $ a_8 = 7x^4 \cdot (4x^2)^{(8-1)} $Simplify exponent: Simplify the exponent in the expression. Calculation: $ a_8 = 7x^4 \cdot (4x^2)^7 $Raise common ratio: Raise the common ratio to the 7th power. Calculation: $ (4x^2)^7 = 4^7 \cdot (x^2)^7 $Calculate values: Calculate the value of $ 4^7 $ and $ (x^2)^7 $. Calculation: $ 4^7 = 16384 $ and $ (x^2)^7 = x^{14} $Multiply first term: Multiply the first term $ 7x^4 $ by the calculated values of $ 4^7 $ and $ x^{14} $. Calculation: $ a_8 = 7x^4 \cdot 16384 \cdot x^{14} $Combine like terms: Combine the like terms to find the 8th term. Calculation: $ a_8 = 7 \cdot 16384 \cdot x^{(4+14)} $Multiply constants: Multiply the constants and add the exponents of $ x $. Calculation: $ a_8 = 114688 \cdot x^{18} $

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Find the 8th term of the geometric sequence shown below.

7x^(4),28x^(6),112x^(8),dots
Answer:

Find the $8$ th term of the geometric sequence shown below. $\newline$ $7 x^{4}, 28 x^{6}, 112 x^{8}, \ldots$ $\newline$ Answer:

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Precalculus

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Q. Find the

8

th term of the geometric sequence shown below.

\newline

7 x^{4}, 28 x^{6}, 112 x^{8}, \ldots

\newline

Answer:

Identify common ratio: Identify the common ratio (r) of the geometric sequence by dividing the second term by the first term. $\newline$ Calculation: $r = \frac{28x^6}{7x^4}$
Calculate common ratio: Simplify the expression to find the common ratio. $\newline$ Calculation: $r = 4x^2$
Use nth term formula: Use the formula for the nth term of a geometric sequence, which is $a_n = a_1 \cdot r^{(n-1)}$ , where $a_1$ is the first term and $n$ is the term number. $\newline$ Calculation: The $8$ th term $a_8 = 7x^4 \cdot (4x^2)^{(8-1)}$
Simplify exponent: Simplify the exponent in the expression. $\newline$ Calculation: $a_8 = 7x^4 \cdot (4x^2)^7$
Raise common ratio: Raise the common ratio to the $7$ th power. $\newline$ Calculation: $(4x^2)^7 = 4^7 \cdot (x^2)^7$
Calculate values: Calculate the value of $4^7$ and $(x^2)^7$ . $\newline$ Calculation: $4^7 = 16384$ and $(x^2)^7 = x^{14}$
Multiply first term: Multiply the first term $7x^4$ by the calculated values of $4^7$ and $x^{14}$ . $\newline$ Calculation: $a_8 = 7x^4 \cdot 16384 \cdot x^{14}$
Combine like terms: Combine the like terms to find the $8$ th term. $\newline$ Calculation: $a_8 = 7 \cdot 16384 \cdot x^{(4+14)}$
Multiply constants: Multiply the constants and add the exponents of $x$ . $\newline$ Calculation: $a_8 = 114688 \cdot x^{18}$