Arithmetic Progressions
Key Points –
AP – 2, 4, 6, 8, 10, 12 _ _ _ _ 100
AP – a1, a2, a3, a4,_ _ _ _ _ an
a1 = a = First term
an = Last term
n = Number of terms
Common difference (d)
d = a2 – a1 = a3 – a2
Finding the nth term –
an = a + (n – 1) d
General form –
AP – a, a + d, a + 2d, a + 3d, a + 4d _ _ _ _
Que. 1. Write the first four terms of the given A.P., when the first term ‘a’ and the common difference ‘d’ are as follows:
1. a = 10 , d = 10
n = 2
an = a + (n – 1) d
a2 = 10 + (2 – 1) 10
a2 = 10 + 1 X 10
a2 = 10 + 10
a2 = 20
n = 3
an = a + (n – 1) d
a3 = 10 + (3 – 1) 10 = 10 + 20
a3 = 30
n = 4
an = a + (n – 1) d
a4 = 10 + (4 – 1) 10 = 10 + 30
a4 = 40
AP = 10, 20, 30, 40 _ _ _ _
2. a = -2 , d = 0
n = 2
an = a + (n – 1) d
a2 = -2 + (2 – 1) 0 = -2 + 0
a2 = -2
n = 3
an = a + (n – 1) d
a3 = -2 + (3 – 1) 0 = -2 + 0
a3 = -2
a4 = -2
AP = -2, -2, -2, -2, _ _ _ _ _ -2
3. a = 4 , d = -3
n = 2
an = a + (n – 1) d
a2 = 4 + (2 – 1) – 3
= 4 + 1 X -3
= 4 + (-3)
= 1
n = 3
an = a + (n – 1) d
a3 = 4 + (3 – 1) – 3
= 4 + 2 X -3
= 4 + (-6)
= -2
n = 4
an = a + (n – 1) d
a4 = 4 + (4 – 1) – 3
= 4 + 3 X -3
= 4 + (-9)
= -5
AP = 4, 1, -2, -5 _ _ _ _ _
5. a = 1.25 , d = 0.25
n = 2
an = a + (n – 1) d
a2 = -1.25 +(2 – 1) X 0.25
a2 = -1.25 + 0.25
a2 = -1.50
n = 3
an = a + (n – 1) d
a3 = -1.25 + (3 – 1) X -0.25
a3 = -1.25 + 0.50
a3 = -1.75
n = 4
an = a + (n – 1) d
a4 = -1.25 + (4 – 1) X -0.25
= -1.25 + 0.75
= -2.00
a4 = -2
AP = -1.25, -1.50, -1.75, -2 _ _ _ _
Que. 2. Write the first term and the common difference for each of the following A.P.s:
1. 3, 1, -1, -3, _ _ _ _
First term (a) = 3
Common difference (d) = a2 – a1
= 1 – 3
= -2
2. -5, -1, 3, 7, _ _ _ _ _
First term (a) = -5
Common difference (d) = a2 – a1
= -1 – 1 (-5)
= -1 + 5
= 4
4. 0.6, 1.7, 2.8, 3.9
(a) = 0.6
(d) = a2 – a1
= 1.7 – 0.6
= 1.1
