In a certain sequence of numbers, each term after the 1 st term is the result of adding 2 to the previous term and multiplying that sum by 3 . If the 4th term in the sequence is 186 , what is the 2 nd term ?

Options

A. 2
B. 4
C. 18
D. 60

Answer

To find the second term in the sequence where each term after the first is obtained by adding 2 to the previous term and then multiplying the result by 3, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Sequence Rule**:
Each term after the first term can be expressed as:
\[ a_{n} = 3(a_{n-1} + 2) \]
where \( a_n \) is the nth term and \( a_{n-1} \) is the previous term.

2. **Given Information**:
We know that the fourth term \( a_4 = 186 \).

3. **Find the Third Term**:
Using the formula, we can express the third term in terms of the fourth term:
\[ a_4 = 3(a_3 + 2) \]
Rearranging gives:
\[ a_3 + 2 = \frac{a_4}{3} \]
Thus,
\[ a_3 = \frac{186}{3} - 2 \]
Calculating this:
\[ a_3 = 62 - 2 = 60 \]

4. **Find the Second Term**:
Now, we can find the second term using the third term:
\[ a_3 = 3(a_2 + 2) \]
Rearranging gives:
\[ a_2 + 2 = \frac{a_3}{3} \]
Thus,
\[ a_2 = \frac{60}{3} - 2 \]
Calculating this:
\[ a_2 = 20 - 2 = 18 \]

5. **Conclusion**:
Therefore, the second term \( a_2 \) is 18.

### Final Answer:
The second term in the sequence is **18**.

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