Let's solve this question step by step.
1. Identify the pattern:
- We know that the first row has 1 student.
- We know that the third row has 5 students.
2. Determine the increment in the number of students per row:
- We observe that from the first row to the third row, the increase in the number of students is from 1 to 5.
- This difference can be noted as follows:
[tex]\[
\text{Difference from Row 1 to Row 3} = 5 - 1 = 4 \text{ students}
\][/tex]
- This difference occurs over two intervals (from Row 1 to Row 2 and from Row 2 to Row 3), so the increment per row is:
[tex]\[
\text{Increment per row} = \frac{4 \text{ students}}{2 \text{ intervals}} = 2 \text{ students per row}
\][/tex]
3. Find the number of students in each row by adding the increment:
- First row: 1 student (given)
- Second row:
[tex]\[
1 + 2 = 3 \text{ students}
\][/tex]
- Third row:
[tex]\[
3 + 2 = 5 \text{ students}
\][/tex]
- We see that this pattern holds.
4. Apply this pattern to find the number of students in the last (8th) row:
- We can generalize the pattern in terms of rows. If [tex]\( n \)[/tex] is the row number, then the number of students in the [tex]\( n \)[/tex]-th row can be written as:
[tex]\[
\text{Students in } n \text{th row} = 1 + (2 \times (n - 1))
\][/tex]
5. Substitute for the 8th row:
- Using [tex]\( n = 8 \)[/tex]:
[tex]\[
\text{Students in 8th row} = 1 + (2 \times (8 - 1)) = 1 + (2 \times 7) = 1 + 14 = 15 \text{ students}
\][/tex]
Thus, the number of students in the last (8th) row is [tex]\( 15 \)[/tex].
