evaluate each function for the given input value.
1. $f(x) = -2x$ for $x = -5$
2. $h(x) = 3x - 1$ for $x = 7$
find the indicated term of each arithmetic sequence.
3. $a_n = 16 + (n - 1)(-0.5)$, $15^{\text{th}}$ term
4. $-8, -6, -4, -2, \dots$, $100^{\text{th}}$ term

Question

Accepted Answer

### Problem 1: Evaluate $ f(x) = -2x $ for $ x = -5 $
# Explanation:
## Step 1: Substitute $ x = -5 $ into $ f(x) $
We have the function $ f(x) = -2x $. To find $ f(-5) $, we replace $ x $ with $ -5 $ in the function. So we get $ f(-5) = -2 \times (-5) $.
## Step 2: Simplify the expression
Multiplying two negative numbers gives a positive result. So $ -2 \times (-5) = 10 $.
# Answer:
$ 10 $

### Problem 2: Evaluate $ h(x) = 3x - 1 $ for $ x = 7 $
# Explanation:
## Step 1: Substitute $ x = 7 $ into $ h(x) $
The function is $ h(x) = 3x - 1 $. Substituting $ x = 7 $, we have $ h(7) = 3\times7 - 1 $.
## Step 2: Simplify the expression
First, calculate $ 3\times7 = 21 $. Then subtract 1 from 21: $ 21 - 1 = 20 $.
# Answer:
$ 20 $

### Problem 3: Find the $ 15^{\text{th}} $ term of the arithmetic sequence $ a_n = 16 + (n - 1)(-0.5) $
# Explanation:
## Step 1: Recall the formula for the $ n^{\text{th}} $ term of an arithmetic sequence
The formula for the $ n^{\text{th}} $ term of an arithmetic sequence is $ a_n = a_1 + (n - 1)d $, where $ a_1 $ is the first term and $ d $ is the common difference. In our given formula $ a_n = 16 + (n - 1)(-0.5) $, to find the $ 15^{\text{th}} $ term, we substitute $ n = 15 $ into the formula. So we get $ a_{15} = 16 + (15 - 1)(-0.5) $.
## Step 2: Simplify the expression inside the parentheses
First, calculate $ 15 - 1 = 14 $. Then our expression becomes $ a_{15} = 16 + 14\times(-0.5) $.
## Step 3: Calculate the product and then the sum
Calculate $ 14\times(-0.5) = -7 $. Then add this to 16: $ 16 + (-7) = 16 - 7 = 9 $.
# Answer:
$ 9 $

### Problem 4: Find the $ 100^{\text{th}} $ term of the arithmetic sequence $ -8, -6, -4, -2, \dots $
# Explanation:
## Step 1: Identify the first term and common difference of the arithmetic sequence
For an arithmetic sequence, the first term $ a_1 $ is the first number in the sequence. Here, $ a_1 = -8 $. The common difference $ d $ is the difference between consecutive terms. Let's take the second term minus the first term: $ -6 - (-8) = -6 + 8 = 2 $. So $ d = 2 $.
## Step 2: Use the formula for the $ n^{\text{th}} $ term of an arithmetic sequence
The formula for the $ n^{\text{th}} $ term of an arithmetic sequence is $ a_n = a_1 + (n - 1)d $. We need to find the $ 100^{\text{th}} $ term, so $ n = 100 $, $ a_1 = -8 $, and $ d = 2 $. Substituting these values into the formula, we get $ a_{100} = -8 + (100 - 1)\times2 $.
## Step 3: Simplify the expression
First, calculate $ 100 - 1 = 99 $. Then calculate $ 99\times2 = 198 $. Now add this to $ -8 $: $ -8 + 198 = 190 $.
# Answer:
$ 190 $

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QUESTION IMAGE

Question

Explanation:

Problem 1: Evaluate \( f(x) = -2x \) for \( x = -5 \)

Step 1: Substitute \( x = -5 \) into \( f(x) \)

Step 2: Simplify the expression

Step 1: Substitute \( x = 7 \) into \( h(x) \)

Step 2: Simplify the expression

Step 1: Recall the formula for the \( n^{\text{th}} \) term of an arithmetic sequence

Step 2: Simplify the expression inside the parentheses

Step 3: Calculate the product and then the sum

Answer:

Problem 2: Evaluate \( h(x) = 3x - 1 \) for \( x = 7 \)