Find the 6th Term in Sequence: 15, 22.5, 30, ...

To determine the 6th element in the sequence, we need to first analyze the pattern of the sequence:

Step 1: Check if the sequence is arithmetic.
Calculate the difference between consecutive terms:

• Difference between 22.5 and 15: $22.5 - 15 = 7.5$
• Difference between 30 and 22.5: $30 - 22.5 = 7.5$

Both differences are equal to $7.5$, indicating that the sequence is arithmetic with a common difference of $d = 7.5$.

Step 2: Find the 6th term of the sequence using the arithmetic sequence formula:
The nth term of an arithmetic sequence is given by $a_n = a_1 + (n-1) \times d$, where $a_1$ is the first term and $d$ is the common difference.

Calculate the 6th term:
$a_6 = 15 + (6-1) \times 7.5$
$a_6 = 15 + 5 \times 7.5$
$a_6 = 15 + 37.5$
$a_6 = 52.5$

Therefore, the 6th element in the sequence is $52.5$. This matches option 3 in the provided choices.