Arithmetic Sequences and Sums

The video tutorial explains an arithmetic sequence starting with the terms 9, 21, 33, and 45, identifying it as an arithmetic sequence due to a common difference of 12. It covers how to find the next term, derive a formula for the nth term, and calculate the sum of the first 90 terms using two methods. The tutorial emphasizes understanding the sequence's structure and applying formulas to solve related problems.

What is the first term of the given arithmetic sequence?

• 33

• 21

• 12

• 9

What is the common difference in the sequence?

• 33

• 21

• 12

• 9

What will be the next term in the sequence after 45?

• 63

• 51

• 69

• 57

Which formula represents the nth term of the sequence?

• a_n = 12n + 9

• a_n = 9n + 12

• a_n = 12 + 9n

• a_n = 9 + 12n

If the first term is a_0, what is the formula for the nth term?

• a_n = a_0 + dn

• a_n = a_0 - dn

• a_n = a_0 / dn

• a_n = a_0 * dn

How many terms are summed to find the sum of the first 90 terms?

• 89

• 91

• 90

• 92

What is the sum of the first 90 terms of the sequence?

• 50000

• 47000

• 45000

• 48870

Which method was used to verify the sum of the sequence?

• Graphical method

• Trial and error

• Algebraic method

• Formula method

What is the last term used in the sum calculation?

• 1086

• 1077

• 1098

• 1065

What is the value of n in the formula S = (n+1)/2 * (a_0 + a_n)?

• 91

• 90

• 89

• 88