Find the 10^th term of the geometric sequence 7,28,112,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.Determine common ratio: Determine the common ratio (r) of the sequence. To find the common ratio, divide the second term by the first term. 28 / 7 = 4 Common Ratio (r): 4Use formula for nth term: Use the formula for the nth term of a geometric sequence. The nth term (a_n) of a geometric sequence can be found using the formula a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.Calculate 10th term: Calculate the 10th term using the formula. a_10 = 7 * 4^(10-1) a_10 = 7 * 4^9Perform exponentiation: Perform the exponentiation. 4^9 = 262144Multiply by first term: Multiply the result by the first term. a_10 = 7 * 262144 a_10 = 1835008

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Find the 10^th term of the geometric sequence
7,28,112,dots
Answer:

Find the $10^{\text {th }}$ term of the geometric sequence $7,28,112, \ldots$ $\newline$ Answer:

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Q. Find the

10^{\text {th }}

term of the geometric sequence

7,28,112, \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.
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. $\newline$ $\frac{28}{7} = 4$ $\newline$ Common Ratio $r$ : $4$
Use formula for nth term: Use the formula for the nth term of a geometric sequence. $\newline$ The nth term $a_n$ of a geometric sequence can be found using the formula $a_n = a_1 \times r^{(n-1)}$ , where $a_1$ is the first term and $r$ is the common ratio.
Calculate $10$ th term: Calculate the $10$ th term using the formula. $\newline$ $a_{10} = 7 \times 4^{10-1}$ $\newline$ $a_{10} = 7 \times 4^9$
Perform exponentiation: Perform the exponentiation. $4^9 = 262144$
Multiply by first term: Multiply the result by the first term. $\newline$ $a_{10} = 7 \times 262144$ $\newline$ $a_{10} = 1835008$