Arithmetic Sequences and Closed Formulas

The video tutorial explains how to analyze an arithmetic sequence, derive its closed formula, and calculate the sum of the series when the last term is given. It also covers finding a closed formula for a related sequence, b sub n, using partial sums from the arithmetic sequence. The tutorial includes step-by-step calculations and verification of the derived formulas.

What is the common difference in the arithmetic sequence discussed?

• 2

• 8

• 3

• 5

Which formula is used to find the nth term of an arithmetic sequence?

• a_n = a_0 + dn

• a_n = a_0 + d(n-1)

• a_n = a_1 + dn

• a_n = a_1 + d(n-1)

What is the closed formula derived for the given arithmetic sequence?

• a_n = 5 + 3n

• a_n = 3 + 2n

• a_n = 5 + 2n

• a_n = 2 + 3n

How many terms are there in the arithmetic series when the last term is 1463?

• 485

• 488

• 486

• 487

What is the sum of the arithmetic series with the last term 1463?

• 357458

• 356458

• 357000

• 358000

What is the first term of the new sequence b_n?

• 0

• 6

• 1

• 5

How is the closed formula for b_n related to the arithmetic sequence?

• It uses the difference of the first n terms of the arithmetic sequence.

• It uses the division of the first n terms of the arithmetic sequence.

• It uses the product of the first n terms of the arithmetic sequence.

• It uses the sum of the first n terms of the arithmetic sequence.

What is the closed formula for b_n?

• b_n = 1 + n/2(6 + 3n)

• b_n = 1 + n/2(7 + 3n)

• b_n = 1 + n/2(5 + 3n)

• b_n = 1 + n/2(8 + 3n)

What is b_1 according to the closed formula for b_n?

• 6

• 7

• 5

• 8

What is b_2 according to the closed formula for b_n?

• 15

• 13

• 12

• 14