The document defines an arithmetic progression as a sequence of numbers where the difference between consecutive terms is constant. Specifically: - An arithmetic progression is a sequence where each term is equal to the previous term plus a constant value, called the common difference. - The formula for the nth term of an arithmetic progression is: tn = a + (n-1)d, where a is the first term and d is the common difference. - The formula to find the sum of the first n terms of an arithmetic progression is: Sn = n/2(t1 + tn), where t1 is the first term and tn is the nth term.

1. ARITHMETIC PROGRESSION

2. SEQUENCE
• Sequence is a list of numbers( or events,
pattern) that are in order.
• E.g 1,2,3,4,5,……..
• *, **, ***, ****,….. Wedding planning…
• We are concerned with mathematical
sequences such as
• 1,2,3,4,5,…………… 2,4,6,8,………………

3. NUMERIC SEQUENCES
SEQUENCE t1 t2 t3 t4 t5 RULE
ARITHMETIC / GEOMETRIC
PROGRESSION
1,3,5,7,9,…. 1 3 5 7 9
ADDING 2 TO ITS
PREVIOUS TERM
ARITHMETIC PROGRESSION
90,88,86,84,82,.. 90 88 86 84 82
ADDING (-2) TO
ITS PREVIOUS
TERM
ARITHMETIC PROGRESSION
4,4,4,4,4,…… 4 4 4 4 4
ADDING 0 TO ITS
PREVIOUS TERM
ARITHMETIC PROGRESSION
2,4,8,16,32,….. 2 4 8 16 32
MULTIPLYING BY
2 with ITS
PREVIOUS TERM
GEOMETRIC PROGRESSION
12, 22,32,42,52,.. 1 4 9 16 25
NO RELATION
WITH ITS
PREVIOUS TERM
NEITHER
If t1 = a and common difference (tn+1 – tn) = d (+, - or 0)
then the arithmetic progression is obtained as
a, (a + d), (a + 2d), (a + 3d), (a + 4d),…

4. ARITHMETIC PROGRESSION
• lets revise:
• Determine whether the following sequences
are A.P? if it is, find next two terms.
2, -2,-6,-10,…
t1 = 2, t2 = -2, t3 = -6, t4 = -10
t2 – t1 = - 2 – (2) = -4
t3 – t2 = - 6 – (-2) = -6 +2 = -4
t4 – t3 = - 10 – (-6) = -10 +6 = -4
The common difference is -4, hence the sequence is A.P
The next two terms are -10-4 =-14 and -14-4 =-18

5. ARITHMETIC PROGRESSION
• Find first three terms of an A.P in the
following cases
** pg 61

6. ARITHMETIC PROGRESSION
ARITHMETIC PROGRESSION
PROCEED TO

7. nth term of an A.P
6, 9, 12, 15, 18, 21,……
t1 t2 t3 ... tn-1 tn tn+1
6 6 + 1x3 6 + 2X3 …. 6 + (n-2)X3 6 +(n-1)X3 6 + (n)X3
In General : nth term tn = a + (n-1)d
tn = a + (n-1) d T3= 6+2X3 = 6+6 =12 T7= 6 + 6X3 = 6 +18= 24 T10 = 6 + 9X3= 33
** PG 66

8. SUM OF FIRST n TERMS OF AN A.P
Sn =
𝑛
2
[2a + (n-1)d or Sn =
𝑛
2
(t1 + tn)
1,3,5,7,… find the sum of first six terms
N =6, a=1, d=2
Sn =
𝑛
2
[2a + (n-1)d
6
2
[2 +5X2]
3[12]
36
1,3,5,7,9,11,13,……
Let find sum of first four
terms:
N =4, t1 = 1, t4 = 7
S4 =
𝑛
2
(t1 + t4)
=
4
2
(1 + 7)
= 16

9. ARITHMETIC PROGRESSION
ARITHMETIC PROGRESSION
2, 5, 8, 11,…..
Sn =
𝑛
2
(t1 + tn)
Sn =
𝑛
2
[2a + (n-1)d]