Arithmetic Basics
Q: What is an arithmetic sequence?
A: A sequence where each term increases or decreases by the same amount (common difference).
Adding or Subtracting
What is a geometric sequence?
A: Each term is multiplied by the same ratio to get the next term.
Arithmetic or Geometric: 10, 20, 30…
Arithmetic
Q: An arithmetic sequence starts at 4, d = 3. Find the 6th term.
A: 19
Q: aₙ = 3n + 2: Is this arithmetic?
A: Yes
Q: Find the common difference: 3, 7, 11, 15
A: 4
Q: Find the common ratio: 2, 4, 8, 16
A: 2
Q: Arithmetic or Geometric: 5, 10, 20…
A: Geometric
Q: A geometric sequence starts at 5, r = 2. Find the 4th term.
A: 40
Q: aₙ = 2·(3)ⁿ⁻¹: Find a₅
A: 162
Q: What’s the 10th term of 5, 8, 11…?
A: 32
Q: What’s the 5th term of 3, 6, 12…?
A: 48
Q: Which type: 81, 27, 9, 3…?
A: Geometric
Q: You save $10, then $20, $30... How much after 12 weeks?
A: 780 (10+20+30+40+50+60+70+80+90+100+110+120)
Q: Find the sum of first 5 terms: 2, 4, 6, 8, 10
A: 30
Q: Find the nth term formula of 2, 5, 8…
A: aₙ = 2+3(n-1)
Q: Find the nth term formula of 1, 3, 9…
A: 1(3)n-1
Q: Which type: 100, 95, 90, 85…?
A: Arithmetic
Q: Bacteria doubles every hour. 1 cell starts. How many after 5 hrs?
A: 32
Q: Find the sum of first 4 terms: 1, 3, 9, 27
A: 40
Q: If a₁ = 7 and d = −2, find a₆
A: −3
Q: If a₁ = 81 and r = 1/3, find a₄
A: 1
Q: Arithmetic or Geometric: 1, 2, 4, 8…
A: Geometric
Q: a₁ = 200, d = −15. What term will be 20?
A: 13
Q: a₁ = 4, r = −2. What is a₆?
A: 4 × (−2)⁵ = 4 × (−32) = −128