Question

An embroidery pattern calls for five stitches in the first row and for three more stitches in each successive row. the 25th row, which is the last row, has 77 stitches. find the total number of stitches in the pattern.

Answer 1

The total number of stitches in the embroidery pattern can be found using the sum formula of an arithmetic sequence, with the calculation resulting in 1025 stitches.

Step-by-step explanation:

The student's question involves finding the total number of stitches in an embroidery pattern that starts with 5 stitches in the first row and increases by 3 stitches per row until the 25th row, which has 77 stitches. This is an arithmetic sequence because the number of stitches increases by a constant amount each row.

To solve this, we can use the formula for the sum (S) of an arithmetic sequence: S = ½ × (n) × (first term + last term), where n is the number of terms. Here, the first term (a1) is 5 stitches, the last term (an) is 77 stitches, and the number of terms (n) is 25 since there are 25 rows.

Plugging the values into the sum formula gives us: S = ½ × (25) × (5 + 77). This simplifies to S = 12.5 × 82, which equals 1025 stitches. Therefore, the total number of stitches in the pattern is 1025.