SME
Grade 9 Math · Problem type
Geometric sequence: the nth term
Use this for “3, 6, 12, … What is the 8th term?”
Chart
Terms: 3, 6, 12, 24, …, 384 (multiply by r = 2 each time).
a₈ = 3 × 2⁷ = 384
This is an example. Type your own values to start a new problem.
aₙ
=
a₁
×
r
−
1
=
e
Number of factors of r
worked out (not typed)
Formulas
e
=
n
−
1
7 = 8 − 1
aₙ
=
a₁
×
r
e
384
=
3
×
2
7
Assumptions
•
Each term multiplies the one before by the same ratio r.
•
The nth term is the first times r, n − 1 times: a₁ × rⁿ⁻¹.
•
A geometric sequence is an exponential function of n.
Step-by-step
WE KNOW
n = 8, a₁ = 3, r = 2
FIND
number of factors of r (e), nth term (aₙ)
Step 1 · Find number of factors of r (e)
Use e = n − 1
From
the
first
term
to
the
nth
there
are
n
−
1
steps,
each
a
factor
of
r
.
e
=
8
−
1
e
=
7
Step 2 · Find nth term (aₙ)
Use aₙ = a₁ × rᵉ
Start
at
the
first
term
and
multiply
by
r
,
e
times.
aₙ
=
3
×
2
7
aₙ = 3 × 128
aₙ = 384
Check
Put the numbers back in. Both sides should match.
7 = 8 − 1 ✓
384
=
3
×
2
7
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.