1. 5.3 Arithmetic Series (1/5)
In an arithmetic series each term increases by a constant amount (d)
This means the difference between consecutive terms is constant (d)
Therefore:
T11 – T10 =
T37 – T36 =
T317 – T316 = d

2. The terms of an arithmetic series are:
+ (a+1d)
+ (a+2d)
+ (a+3d)
+ …
+ [a+(n-1)d]
+ …
Tn = a + (n – 1) d
Value of
nth term
1st term
Common
Difference
Term
number

3. Find the 101th term of the series
5.3 Arithmetic Series (3/5)
Find the 101th term of the series …
a = 3
n = 101
d = 11 – 7 = 4
Tn = a + (n – 1) d
= 3 + (101 – 1) 4
= 403

4. What is the nth term of the series
5.3 Arithmetic Series (4/5)
What is the nth term of the series …
a = 1
d = 13 – 7 = 6
Tn = a + (n – 1) d
= 1 + (n – 1) 6
= 1 + 6n – 6
Tn= 6n – 5

5. Which term of the series is 189 .
5.3 Arithmetic Series (5/5)
Which term of the series is 189 . …
Tn = a + (n – 1) d
a = 9
189 = 9 + (n – 1) 5
Tn = 189
189 = 9 + 5n – 5
189 = 5n + 4
d = 16 – 9
5n = 185 =5
n = 36