Equations of Arithmetic Sequences

What defines an arithmetic sequence?

• A sequence where numbers are multiplied by a constant.

• A sequence where numbers decrease over time.

• A sequence where the same value is added or subtracted each time.

• A sequence of random values.

What is the formula for the nth term of the sequence 5, 9, 13, 17, 21?

• 4n - 1

• 5n - 1

• n + 4

• 4n + 1

How do you find the 50th term of the sequence 5, 9, 13, 17, 21?

• Subtract 4 from 5, fifty times.

• Multiply 50 by 5.

• Use the formula 4n + 1 with n = 50.

• Add 4 to 21 repeatedly until reaching the 50th term.

What is the common difference in the sequence 5, 9, 13, 17, 21?

• 5

• 3

• 4

• 2

How is the term '4n + 1' derived for the sequence 5, 9, 13, 17, 21?

• By adding 4 to each term starting from 5.

• By setting n = 1 for the first term and solving.

• By identifying the common difference and calculating the offset from an imaginary zero term.

• By multiplying each term by 4 and adding 1.

What would be the first term if you used the formula '4n + 1' with n = 0?

• 0

• 1

• 5

• 4

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

• The difference between the highest and lowest terms.

• The most frequently occurring number in the sequence.

• The value added to each term to get the next term.

• The average value of all terms.

For the sequence decreasing by 5 each time, starting at 26, what is the formula for the nth term?

• -5n - 26

• 5n - 31

• 31 - 5n

• -5n + 31

How do you verify if the formula '1.5n - 0.5' is correct for a sequence?

• Substitute n = 1 and check the first term.

• Divide each term by 1.5 and subtract 0.5.

• Use the formula to calculate a known term in the sequence and compare.

• Add 1.5 to each term and see if it matches.

What is the fifth term of the sequence defined by the formula '1.5n - 0.5'?

• 6.5

• 7.5

• 7

• 8