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 Given the 1st term is 5 & d = 2, what is the 2nd term?
-- Answer -- 7
1st term = 5, d = 2
sequence: 5, 7, 9, 11, 13, 15 …
2nd term is 7
Question 2 Given the set of numbers 1, 6, 11, 16. What is the difference? What is the 8th term or a₈?
-- Answer -- difference (d) = 6, 6th term (a₈) = 36
d = 5 (6 - 1 or 11 - 6, etc)
sequence: 1 6 11 16 21 26 31 36 41 …
8th term = 36
Question 3 There are 220 people in a theatre. How many rows will be needed if the first row holds 10 seats and each succeeding row has 2 more seats than the previous row?
-- Answer -- 11
a₁ = 10 and d = 2
aₙ = 10 + 2(n - 1) = 2n + 8
sₙ = (a₁ + aₙ) / 2 * n = (10 + 2n + 8) / 2 * n = 220
n = 11
ACT PRACTICE PROBLEMS