which term of the arithmetic sequence is -18, given that a1=7 and a2=2?

In an arithmetic sequence, the general formula for the \(n\)-th term is:

\[
a_n = a_1 + (n-1) \cdot d
\]

where:
- \(a_n\) is the \(n\)-th term,
- \(a_1\) is the first term,
- \(d\) is the common difference between consecutive terms,
- \(n\) is the term number.

### Step 1: Find the common difference \(d\)
We are given:
- \(a_1 = 7\),
- \(a_2 = 2\).

The common difference \(d\) can be calculated as:

\[
d = a_2 - a_1 = 2 - 7 = -5
\]

### Step 2: Use the formula to find \(n\) when \(a_n = -18\)
We now want to find which term \(n\) gives \(a_n = -18\). Using the general formula for \(a_n\):

\[
a_n = a_1 + (n-1) \cdot d
\]

Substitute the known values:

\[
-18 = 7 + (n-1) \cdot (-5)
\]

### Step 3: Solve for \(n\)
Simplify the equation:

\[
-18 = 7 - 5(n-1)
\]

\[
-18 = 7 - 5n + 5
\]

\[
-18 = 12 - 5n
\]

\[
-18 - 12 = -5n
\]

\[
-30 = -5n
\]

\[
n = \frac{30}{5} = 6
\]

Thus, the \(6\)-th term of the arithmetic sequence is \(-18\).

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Would you like further details or have any questions?

Here are 5 related questions for you:
1. How do you calculate the sum of the first \(n\) terms of an arithmetic sequence?
2. What is the formula for the common difference in an arithmetic sequence?
3. How can we find the \(n\)-th term if the sequence has a positive common difference?
4. Can you explain how an arithmetic sequence differs from a geometric sequence?
5. How does knowing two terms in an arithmetic sequence help in finding others?

**Tip:** When solving for unknowns in arithmetic sequences, identifying the common difference is crucial—it drives how fast the terms grow or shrink.

Which term of the arithmetic sequence is -18, given that a1=7 and a2=2?

Discover how to find which term of the arithmetic sequence is -18, given that a1=7 and a2=2. Learn the step-by-step method to calculate the common difference and apply the general formula for arithmetic sequences. Suitable for Grades 8-10.

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