The twelfth term of an anithmetic sequence is 5 and the common difference of the sequence
is 3
(a) Determine which term has a value of 47

Question

The twelfth term of an anithmetic sequence is 5 and the common difference of the sequence is 3 (a) Determine which term has a value of 47

UpStudy AI · Accepted Answer

To determine which term of the arithmetic sequence has a value of **47**, let's follow these steps:

### Given:
- **Twelfth term ($$a_{12}$$)**: 5
- **Common difference ($$d$$)**: 3

### Formula for the $$n^{th}$$ term of an arithmetic sequence:
$$
a_n = a_1 + (n - 1) \times d
$$
where:
- $$a_n$$ is the $$n^{th}$$ term,
- $$a_1$$ is the first term,
- $$d$$ is the common difference,
- $$n$$ is the term number.

### Step 1: Find the first term ($$a_1$$)
Given $$a_{12} = 5$$ and $$d = 3$$,
$$
a_{12} = a_1 + (12 - 1) \times 3
$$
$$
5 = a_1 + 33
$$
$$
a_1 = 5 - 33
$$
$$
a_1 = -28
$$

### Step 2: Find the term number ($$n$$) when $$a_n = 47$$
Using the formula:
$$
47 = -28 + (n - 1) \times 3
$$
$$
47 + 28 = (n - 1) \times 3
$$
$$
75 = 3(n - 1)
$$
$$
n - 1 = \frac{75}{3}
$$
$$
n - 1 = 25
$$
$$
n = 26
$$

### **Answer:**
The **26th term** of the arithmetic sequence is **47**.
The 26th term of the sequence is 47.

The twelfth term of an anithmetic sequence is 5 and the common difference of the sequence
is 3
(a) Determine which term has a value of 47

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