SME
Grade 9 Math · Algebra 1
Arithmetic and geometric sequences
Use this for “7, 11, 15, 19, … What is the 100th term?”
Chart
Terms: 7, 11, 15, 19, …, 403 (add d = 4 each time).
a₁₀₀ = 7 + 99 × 4 = 403
The chart skips from n = 6 to n = 100.
This is an example. Type your own values to start a new problem.
aₙ
=
a₁
+
d
(
n
−
1)
=
Formulas
aₙ
=
a₁
+
(
n
−
1)
×
d
403 = 7 + (100 − 1) × 4
Assumptions
•
Each term adds the same difference d to the one before.
•
n counts the terms from 1, so the nth term is n − 1 steps past the first.
•
An arithmetic sequence is a linear function of n, with slope d.
Step-by-step
WE KNOW
n = 100, a₁ = 7, d = 4
FIND
nth term (aₙ)
Step 1 · Find nth term (aₙ)
Use aₙ = a₁ + (n − 1) × d
Start
at
the
first
term
and
add
n
−
1
differences.
aₙ = 7 + (100 − 1) × 4
aₙ = 7 + 99 × 4
aₙ = 7 + 396
aₙ = 403
Check
Put the numbers back in. Both sides should match.
403 = 7 + (100 − 1) × 4 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.