2. What is the term $$ a_{8} $$ of the sequence $$ \left\{a_{n} ight\} $$ if $$ a_{n} $$ equals $$ \begin{array}{ll} ext { a) } 2^{n-1} ? & ext { b) } 7 ext { ? } \ ext { c) } 1+(-1)^{n} ? & ext { d) }-(-2)^{n} ?\end{array} $$

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2. What is the term $$ a_{8} $$ of the sequence $$ \left\{a_{n}ight\} $$ if $$ a_{n} $$ equals $$ \begin{array}{ll}	ext { a) } 2^{n-1} ? & 	ext { b) } 7 	ext { ? } \ 	ext { c) } 1+(-1)^{n} ? & 	ext { d) }-(-2)^{n} ?\end{array} $$

UpStudy AI · Accepted Answer

Let's calculate the 8th term $$ a_8 $$ for each of the given sequences:

### a) $$ a_n = 2^{n-1} $$
To find $$ a_8 $$:
$$
a_8 = 2^{8-1} = 2^7 = 128
$$

### b) $$ a_n = 7 $$
This is a constant sequence, meaning every term is 7:
$$
a_8 = 7
$$

### c) $$ a_n = 1 + (-1)^n $$
To find $$ a_8 $$:
$$
a_8 = 1 + (-1)^8 = 1 + 1 = 2
$$
*Since $$ (-1)^8 = 1 $$ because the exponent is even.*

### d) $$ a_n = -(-2)^n $$
To find $$ a_8 $$:
$$
a_8 = -(-2)^8 = -256
$$
*Explanation: $$ (-2)^8 = 256 $$ (even exponent), and applying the negative sign gives $$ -256 $$.*

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**Summary of $$ a_8 $$ for each sequence:**
- **a)** $$ 128 $$
- **b)** $$ 7 $$
- **c)** $$ 2 $$
- **d)** $$ -256 $$
The 8th term $$ a_8 $$ for each sequence is: - a) 128 - b) 7 - c) 2 - d) -256

What is the term of the sequence if
equals

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What is the term of the sequence if equals