ARITHMETIC

PROGRESSIONS

• Identifying whether a given list of

numbers is A.P. or not

1) Which of the following are APs ?

i) 2, 4, 8, 16, …

Sol:

In an AP difference between any two consecutive terms is constant

a₁ = 2,

a₂ – a₁

= 4 – 2

= 2

a₃ – a₂

= 8 – 4

= 4

• As difference is not constant, the

given list of numbers is not an AP.

a₂ = 4,

a₃ = 8,

a₄ = 16

Exercise 5.1 4(i)

1) Which of the following are APs ?

ii) -10, -6, -2, 2, …

Sol:

In an AP difference between any two consecutive terms is constant

a₁ = -10,

• As difference is constant, the

given list of numbers is an AP.

a₂ = -6,

a₃ = -2,

a₄ = 2

a₂ – a₁

= -6 – (-10)

= -6 + 10

a₃ – a₂

= -2 – (-6)

= - 2 + 6

= 4

= 4

a₄ – a₃

= 2 – (-2)

= 2 + 2

= 4

Exercise 5.1 4(iv)

1) Which of the following are APs ?

a₃ = 0.222,

iii) 0.2, 0.22, 0.222, 0.2222, …

Sol:

a₁ = 0.2,

a₂ – a₁

= 0.22 – 0.2

= 0.02

a₃ – a₂

= 0.222 – 0.22

= 0.002

• As difference is not constant, the

given list of numbers is not an AP.

a₂ = 0.22,

a₄ = 0.2222

In an AP difference between any two consecutive terms is constant

Exercise 5.1 4(vi)

1) Which of the following are APs ?

iv) 0, -4, -8, -12, …

Sol:

a₁ = 0,

• As difference is constant, the

given list of numbers is an AP.

a₂ = -4,

a₃ = -8,

a₄ = -12

a₂ – a₁

= -4 – 0

a₃ – a₂

= -8 – (-4)

= -8 + 4

= - 4

= - 4

a₄ – a₃

= -12 – (-8)

= - 4

= -12 + 8

In an AP difference between any two consecutive terms is constant

Exercise 5.1 4(vii)