Step 1 of 4 · The trick
An arithmetic sequence adds the same amount each step. Find that amount, plug into the formula.
3, 7, 11, 15, ... · jumps by +4 every time, so d = 4.
Formula: aₙ = a₁ + (n − 1) · d
Plug in a₁ = 3, d = 4 · simplify → aₙ = 4n − 1.
Once you have the formula, any term is one multiplication + one subtraction away.
Step 2 of 4 · 3, 7, 11, 15, ...
Check
a₁ = 4(1) − 1 = 3 ✓
a₂ = 4(2) − 1 = 7 ✓
a₁₀ = 4(10) − 1 = 39
3, 7, 11, 15, ... → aₙ = 4n − 1
Step 3 of 4 · 50, 47, 44, 41, ... (negative d)
Check
a₁ = −3(1) + 53 = 50 ✓
a₄ = −3(4) + 53 = 41 ✓
a₁₂ = −3(12) + 53 = 17
50, 47, 44, 41, ... → aₙ = −3n + 53
Step 4 of 4 · Your turn
Use the formula aₙ = a₁ + (n − 1) · d.
🏆
Nice work!
nth-term formulas — solved.