Geometric and Arithmetic Sequences

The video tutorial covers arithmetic and geometric sequences, explaining how to find the nth term and the sum of terms for each type. It begins with arithmetic sequences, defining the nth term as 'a + (n-1)d' and the sum as 'n/2 * (first term + last term)'. The tutorial then introduces geometric sequences, defining the nth term as 'a * r^(n-1)' and the sum as 'a * (1 - r^n) / (1 - r)'. Key concepts include understanding common differences and ratios, and applying formulas to calculate terms and sums.

What is the first term in the arithmetic sequence 3, 5, 7, 9?

• 9

• 3

• 5

• 7

What is the common difference in the sequence 3, 5, 7, 9?

• 4

• 2

• 3

• 1

How can the second term in an arithmetic sequence be expressed?

• a + 3d

• a + 4d

• a + 2d

• a + d

What is the formula for the nth term in an arithmetic sequence?

• a + 3nd

• a + (n-1)d

• a + nd

• a + 2nd

Why is the formula for the nth term in an arithmetic sequence 'a + (n-1)d'?

• Because the sequence starts at 0

• Because the sequence starts at 1

• Because the sequence starts at n

• Because the sequence starts at d

What is the nth term in an arithmetic sequence if the first term is 4 and the common difference is 3?

• 4 + 3n-1

• 4 + 3(n-1)

• 4 + (n-1)3

• 4 + 3n

How do you find the sum of terms in an arithmetic sequence?

• Multiply the first term by n

• Add the first and last term, then divide by 2 and multiply by n

• Multiply the first and last term

• Add the first and last term, then multiply by n

What is the average of n terms in an arithmetic sequence?

• Sum of first and last term divided by 2

• Sum of terms divided by n

• Sum of terms divided by 2

• Sum of first and last term divided by n

What is the sum of terms in a sequence called?

• Series

• Product

• Quotient

• Difference

What defines a geometric sequence?

• A constant ratio between terms

• A constant sum between terms

• A constant difference between terms

• A constant product between terms