Find the 8^th term of the geometric sequence 5,20,80,dots Answer:

Identify type of sequence: Identify the type of sequence. The given sequence is geometric because each term after the first is found by multiplying the previous term by a constant ratio.Determine common ratio: Determine the common ratio (r) of the sequence. To find the common ratio, divide the second term by the first term. r = 20 / 5 = 4Use formula for nth term: Use the formula for the nth term of a geometric sequence. The nth term (T_n) of a geometric sequence can be found using the formula T_n = a * r^(n-1), where a is the first term and n is the term number.Calculate 8th term: Calculate the 8th term using the formula. T_8 = 5 * 4^(8-1) = 5 * 4^7Perform exponentiation: Perform the exponentiation. 4^7 = 4 * 4 * 4 * 4 * 4 * 4 * 4 = 16384Multiply by first term: Multiply the result by the first term. T_8 = 5 * 16384 = 81920

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Find the 8^th term of the geometric sequence
5,20,80,dots
Answer:

Find the $8^{\text {th }}$ term of the geometric sequence $5,20,80, \ldots$ $\newline$ Answer:

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Q. Find the

8^{\text {th }}

term of the geometric sequence

5,20,80, \ldots

\newline

Answer:

Identify type of sequence: Identify the type of sequence. $\newline$ The given sequence is geometric because each term after the first is found by multiplying the previous term by a constant ratio.
Determine common ratio: Determine the common ratio $r$ of the sequence. $\newline$ To find the common ratio, divide the second term by the first term. $\newline$ $r = \frac{20}{5} = 4$
Use formula for nth term: Use the formula for the nth term of a geometric sequence. $\newline$ The nth term $T_n$ of a geometric sequence can be found using the formula $T_n = a \cdot r^{(n-1)}$ , where $a$ is the first term and $n$ is the term number.
Calculate $8$ th term: Calculate the $8$ th term using the formula. $T_8 = 5 \times 4^{8-1} = 5 \times 4^7$
Perform exponentiation: Perform the exponentiation. $4^7 = 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 = 16384$
Multiply by first term: Multiply the result by the first term. $\newline$ $T_8 = 5 \times 16384 = 81920$