What are the formulas for arithmetic and geometric sequences

The video tutorial covers arithmetic and geometric sequences, explaining their respective formulas for the n-th term and partial sums. It highlights the differences between arithmetic and geometric sequences, particularly in terms of infinite sums. The tutorial emphasizes the importance of understanding these formulas for quick application.

What is the formula for the n-th term in an arithmetic sequence?

• a_n = a_1 + r^(n-1)

• a_n = a_1 * (n - 1) * d

• a_n = a_1 * r^(n-1)

• a_n = a_1 + (n - 1) * d

In a geometric sequence, what does the variable 'r' represent?

• The product of terms

• The ratio between terms

• The difference between terms

• The sum of terms

How is the partial sum of a geometric sequence calculated?

• S_n = n/2 * (a_1 + a_n)

• S_n = a_1 * (1 - r^n) / (1 - r)

• S_n = a_1 + (n - 1) * d

• S_n = a_1 * r^(n-1)

What is the formula for the sum of an infinite geometric sequence?

• S = n/2 * (a_1 + a_n)

• S = a_1 + (n - 1) * d

• S = a_1 * (1 - r^n) / (1 - r)

• S = a_1 / (1 - r)

Which of the following is true about the sum of a finite geometric sequence?

• It does not depend on the ratio 'r'

• It is calculated using S_n = a_1 * (1 - r^n) / (1 - r)

• It is always greater than the sum of an infinite sequence

• It can be calculated using S = a_1 / (1 - r)