Question

for each sequence, determine whether it appears to be arithmetic. if it does, find the common difference. 9, 2, -5, -12,... \bigcirc arithmetic \quad common difference: $d = \square$ \bigcirc not arithmetic -2, -4, -8, -16,... \bigcirc arithmetic \quad common difference: $d = \square$ \bigcirc not arithmetic 17, 19, 22, 25,... \bigcirc arithmetic \quad common difference: $d = \square$ \bigcirc not arithmetic

Explanation:

First Sequence: \( 9, 2, -5, -12, \dots \)

Step 1: Check the difference between the second and first term

To find the difference, subtract the first term from the second term. So, \( 2 - 9 = -7 \).

Step 2: Check the difference between the third and second term

Subtract the second term from the third term: \( -5 - 2 = -7 \).

Step 3: Check the difference between the fourth and third term

Subtract the third term from the fourth term: \( -12 - (-5) = -12 + 5 = -7 \).
Since the difference between consecutive terms is constant (\( -7 \)), the sequence is arithmetic with a common difference \( d = -7 \).

Second Sequence: \( -2, -4, -8, -16, \dots \)

Step 1: Check the difference between the second and first term

Subtract the first term from the second term: \( -4 - (-2) = -4 + 2 = -2 \).

Step 2: Check the difference between the third and second term

Subtract the second term from the third term: \( -8 - (-4) = -8 + 4 = -4 \).
Since \( -2
eq -4 \), the difference between consecutive terms is not constant. So, the sequence is not arithmetic.

Third Sequence: \( 17, 19, 22, 25, \dots \)

Step 1: Check the difference between the second and first term

Subtract the first term from the second term: \( 19 - 17 = 2 \).

Step 2: Check the difference between the third and second term

Subtract the second term from the third term: \( 22 - 19 = 3 \).
Since \( 2
eq 3 \), the difference between consecutive terms is not constant. So, the sequence is not arithmetic.

Answer:

s:

• For the sequence \( 9, 2, -5, -12, \dots \): Arithmetic, Common difference: \( d = -7 \)
• For the sequence \( -2, -4, -8, -16, \dots \): Not arithmetic
• For the sequence \( 17, 19, 22, 25, \dots \): Not arithmetic