Math Snap

STEP 1

1. The sequence alternates between positive and negative terms.
2. The sequence is arithmetic with a common difference.
3. The sequence starts at 6 and ends at 18.

STEP 2

1. Identify the pattern in the sequence.
2. Determine the general formula for the sequence.
3. Write the sequence in sigma notation.
4. Identify the values of $A$ and $B$.

STEP 3

Observe the sequence: $6, -8, 10, -12, 14, -16, 18$.
The sequence alternates signs and increases by 2 in absolute value.

STEP 4

Identify the general formula for the sequence.
The sequence can be split into two parts: positive and negative.
Positive terms: $6, 10, 14, 18$ which can be written as $a_n = 6 + 4(n-1)$.
Negative terms: $-8, -12, -16$ which can be written as $b_n = -(8 + 4(n-1))$.

STEP 5

Combine the sequences into a single formula using sigma notation.
The sequence can be expressed as:
$$\sum_{n=1}^{4} (6 + 4(n-1)) - \sum_{n=1}^{3} (8 + 4(n-1))$$

Identify the values of $A$ and $B$.
The number of terms in the sequence is 7, so $A = 7$.
The sequence alternates, so $B$ represents the alternating sign pattern, which is $(-1)^{n+1}$.
The sigma notation for the sequence is:
$$\sum_{n=1}^{7} (-1)^{n+1} (6 + 2(n-1))$$ Values:
$$\begin{array}{l} A= 7 \\ B= (-1)^{n+1} \end{array}$$