Learn how to write the rule of an arithmetic sequence given a sequence

The video tutorial explains how to find the number of terms in an arithmetic sequence using the sum formula. It begins by introducing the sum formula and determining the type of sequence. The teacher then guides students through identifying the common difference and applying the formula to find the number of terms. The session concludes with clarifications and addressing student questions.

What is the main characteristic of an arithmetic sequence?

• It has a common ratio.

• It has a common difference.

• It has a variable difference.

• It has a constant ratio.

Which formula is used to find the number of terms in an arithmetic sequence?

• a_n = a_1 + (n-1) * d

• S_n = n/2 * (a_1 + a_n)

• S_n = a_1 * (1-r^n)/(1-r)

• a_n = a_1 * r^(n-1)

If the first term of an arithmetic sequence is 8 and the common difference is 1, what is the formula for the nth term?

• a_n = 8 - n

• a_n = 8 * n

• a_n = 8 + n

• a_n = 8 + (n-1) * 1

What is the value of a_n if a_1 is 8 and the common difference is 1, and n is 8?

• 16

• 8

• 7

• 15

In the context of arithmetic sequences, what does the variable 'd' represent?

• The last term

• The first term

• The common ratio

• The common difference