SME
Grade 11 Math · Problem type
Arithmetic series
Use this for “Find the sum of the first 10 terms of 5, 9, 13, ….”
Chart
Terms: 5, 9, 13, 17, …, 41 (add d = 4 each time).
a₁₀ = 5 + 9 × 4 = 41
S₁₀
=
10
×
5 + 41
2
=
230
This is an example. Type your own values to start a new problem.
aₙ
=
a₁
+
(
n
−
1)
×
d
Sₙ
=
n
×
(
a₁
+
aₙ
)
÷
2
Formulas
aₙ
=
a₁
+
(
n
−
1)
×
d
41 = 5 + (10 − 1) × 4
Sₙ
=
n
×
a₁
+ aₙ
2
230
=
10
×
5 + 41
2
Assumptions
•
The terms go up by the same common difference d each time.
•
Pair the first and last terms, the second and second-to-last, and so on: each pair adds to a₁ + aₙ.
•
n terms make n ÷ 2 pairs, so Sₙ = n(a₁ + aₙ) ÷ 2.
Step-by-step
WE KNOW
a₁ = 5, d = 4, n = 10
FIND
last term (aₙ), sum of the n terms (Sₙ)
Step 1 · Find last term (aₙ)
Use aₙ = a₁ + (n − 1) × d
From
the
first
term,
n
−
1
steps
of
d
.
aₙ = 5 + (10 − 1) × 4
aₙ = 5 + 9 × 4
aₙ = 5 + 36
aₙ = 41
Step 2 · Find sum of the n terms (Sₙ)
Use Sₙ = n × (a₁ + aₙ) ÷ 2
n
2
pairs,
each
adding
to
a₁
+
aₙ.
Sₙ
=
10
×
5 + 41
2
Sₙ
=
10
×
46
2
Sₙ
=
460
2
Sₙ = 230
Check
Put the numbers back in. Both sides should match.
41 = 5 + (10 − 1) × 4 ✓
230
=
10
×
5 + 41
2
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.