Find the 10^th term of the geometric sequence 1,-2,4,dots Answer:

Identify Sequence Type: Identify the type of sequence. The given sequence alternates signs and each term is twice the absolute value of the previous term, which indicates it is a geometric sequence.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 = (-2) / 1 = -2Use Geometric Sequence Formula: 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 10th Term: Calculate the 10th term using the formula. T_10 = 1 * (-2)^(10-1) T_10 = 1 * (-2)^9 T_10 = 1 * (-512) T_10 = -512

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Find the 10^th term of the geometric sequence
1,-2,4,dots
Answer:

Find the $10^{\text {th }}$ term of the geometric sequence $1,-2,4, \ldots$ $\newline$ Answer:

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Q. Find the

10^{\text {th }}

term of the geometric sequence

1,-2,4, \ldots

\newline

Answer:

Identify Sequence Type: Identify the type of sequence. The given sequence alternates signs and each term is twice the absolute value of the previous term, which indicates it is a geometric sequence.
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. $\newline$ $r = \frac{-2}{1} = -2$
Use Geometric Sequence Formula: 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 $10$ th Term: Calculate the $10$ th term using the formula. $\newline$ $T_{10} = 1 \times (-2)^{10-1}$ $\newline$ $T_{10} = 1 \times (-2)^9$ $\newline$ $T_{10} = 1 \times (-512)$ $\newline$ $T_{10} = -512$