Arithmetic Sequences

CONCEPTS

Arithmetic Sequence

• A series of numbers changes with the same difference

• Look for words, "arithmetic sequence" or "constant difference" in the question

Arithmetic Sequence: series of numbers with a constant difference (d)

• d = aₙ – aₙ₋₁

• aₙ = a₁ + (n – 1) * d

EXAMPLES

Given the sequence, what is the difference?

1,3,5 => difference = 2

2,5,8 => difference = 3

PRACTICE PROBLEMS

Question 1 The 4th term is 16. The 10th term is 27. What's d?

-- Answer -- 11/6

Method 1

d = (27 – 16) / (10 – 4) = 11/6

Method 2

Term Number Difference

4 16

5 16 + d

6 16 + 2d

7 16 + 3d

8 16 + 4d

9 16 + 5d

10 27 16 + 6d

16 + 6d = 27, d = 11/6

Question 2 What is the 1st term in the sequence above?

-- Answer -- 11.5

aₙ = a₁ + (n – 1) * d =, 16 = a₁ + (4 – 1) * 11/6

a₁ = 16 – 3 * 11/6 = 16 – 5.5 = 11.5

ACT PRACTICE PROBLEMS

1/1

1/1