Find the 8^th term of the geometric sequence 4,-12,36,dots Answer:

Find Common Ratio: To find the 8th term of a geometric sequence, we need to know the common ratio. The common ratio (r) is the factor by which we multiply one term to get the next term. We can find the common ratio by dividing the second term by the first term. r = (-12) / 4Calculate Common Ratio: Now, let's calculate the common ratio using the values from the sequence. r = (-12) / 4 = -3Use Geometric Sequence Formula: With the common ratio found, we can use the formula for the nth term of a geometric sequence, which is a_n = a_1 * r^(n-1), where a_1 is the first term and n is the term number. For the 8th term (a_8), we have: a_8 = 4 * (-3)^(8-1)Calculate Exponent: Now we calculate the exponent part of the formula. (-3)^(8-1) = (-3)^7Calculate (-3)^7: Calculating (-3)^7 gives us: (-3)^7 = -3 * -3 * -3 * -3 * -3 * -3 * -3 = -2187Multiply First Term: Now we multiply the first term of the sequence by the result of the exponent calculation to find the 8th term. a_8 = 4 * (-2187)Find 8th Term: Multiplying 4 by -2187 gives us the 8th term of the sequence. a_8 = 4 * (-2187) = -8748

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Find the 8^th term of the geometric sequence
4,-12,36,dots
Answer:

Find the $8^{\text {th }}$ term of the geometric sequence $4,-12,36, \ldots$ $\newline$ Answer:

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Q. Find the

8^{\text {th }}

term of the geometric sequence

4,-12,36, \ldots

\newline

Answer:

Find Common Ratio: To find the $8^{\text{th}}$ term of a geometric sequence, we need to know the common ratio. The common ratio ( $r$ ) is the factor by which we multiply one term to get the next term. $\newline$ We can find the common ratio by dividing the second term by the first term. $\newline$ $r = \frac{-12}{4}$
Calculate Common Ratio: Now, let's calculate the common ratio using the values from the sequence. $r = (-12) / 4 = -3$
Use Geometric Sequence Formula: With the common ratio found, we can use the formula for the nth term of a geometric sequence, which is $a_n = a_1 \times r^{(n-1)}$ , where $a_1$ is the first term and $n$ is the term number. $\newline$ For the $8$ th term ( $a_8$ ), we have: $\newline$ $a_8 = 4 \times (-3)^{(8-1)}$
Calculate Exponent: Now we calculate the exponent part of the formula. $(-3)^{8-1} = (-3)^7$
Calculate $(-3)^7$ : Calculating $(-3)^7$ gives us: $\newline$ $(-3)^7 = -3 \times -3 \times -3 \times -3 \times -3 \times -3 \times -3 = -2187$
Multiply First Term: Now we multiply the first term of the sequence by the result of the exponent calculation to find the $8^{\text{th}}$ term. $a_8 = 4 \times (-2187)$
Find $8$ th Term: Multiplying $4$ by $-2187$ gives us the $8$ th term of the sequence. $\newline$ $a_8 = 4 \times (-2187) = -8748$