Exploring Arithmetic Sequences in Algebra

What defines an arithmetic sequence?

• A sequence where each term is derived by adding a constant

• A sequence where each term decreases by a division factor

• A sequence of randomly ordered numbers

• A sequence where each term increases by a multiplication factor

What is the common difference in the sequence 4, 6, 8, 10?

• 6

• 4

• 2

• 8

What does the term 'common difference' refer to in an arithmetic sequence?

• The constant addition or subtraction between consecutive terms

• The product of the first and last terms

• The ratio of consecutive terms

• The difference between the highest and lowest terms

How is the nth term of an arithmetic sequence calculated?

• a_n = a_1 * n + d

• a_n = a_1 / (n - 1) + d

• a_n = a_1 + (n - 1) / d

• a_n = a_1 + (n - 1) * d

If the first term of a sequence is 1 and the common difference is 9, what is the formula for the nth term?

• a_n = 1 + 9n

• a_n = 9 + (n - 1) * 1

• a_n = (n - 1) + 9

• a_n = 1 + (n - 1) * 9

What is the 22nd term of the sequence defined by the equation a_n = 1 + (n - 1) * 9?

• 211

• 205

• 198

• 190

How do you find the nth term of a sequence using its formula?

• Substitute the value of n into the formula

• Multiply the first term by n

• Add the common difference to the first term n times

• Divide the first term by the common difference

What is the 100th term of the sequence where a_n = 2n + 3?

• 203

• 230

• 200

• 233

If the nth term of a sequence is 97, how do you find n?

• Substitute 97 for a_n in the equation and solve for n

• Add 97 to each term until you reach n

• Multiply each term by n until you reach 97

• Divide each term by n until you reach 97

Which term of the sequence is 172 if the sequence's formula is plugged into a_n = 172?

• 30th term

• 25th term

• 22nd term

• 20th term