Find the partial sum of a sequence of 25 terms

The video tutorial explains how to find the partial sum of an arithmetic sequence. It begins by introducing the concept of partial sums and the need for a formula to calculate them efficiently. The teacher then demonstrates how to derive the rule for the sequence using the difference between terms. The formula for the partial sum is applied to find the 25th term and calculate the sum of the sequence. The tutorial concludes with a practical example of calculating the sum using the derived formula.

What is the pattern observed in the sequence described by the teacher?

• Subtracting 3 from each term

• Adding 6 to each term

• Adding 5 to each term

• Multiplying each term by 2

Why is it impractical to sum a large number of terms manually?

• It leads to incorrect results

• It is impossible to do without a computer

• It is time-consuming

• It requires complex calculations

What is the formula for the partial sum of an arithmetic sequence?

• n * (a1 - an)

• n * (a1 + an)

• n / 2 * (a1 + an)

• n / 2 * (a1 - an)

What is the first step in finding the rule for an arithmetic sequence?

• Determine the common difference

• Find the last term

• Calculate the sum of terms

• Identify the first term

What is the derived rule for the sequence in the lesson?

• a_n = 6n + 2

• a_n = 6n - 4

• a_n = 2n + 6

• a_n = 4n + 6

How is the 25th term of the sequence calculated?

• 25 / 6 + 4

• 6 * 25 - 4

• 6 * 25 + 4

• 25 / 6 - 4

What is the sum of the first 25 terms of the sequence?

• 1800

• 1750

• 1850

• 1900