AP GP HP

Question 1

To find nᵗʰ term, Tₙ (in AP) =

Answer 1

a+(n-1)d

Question 2

What is a, d, n, r

Answer 2

a = first term
d = common difference
n = term number
r = Common ratio

Question 3

What is Tₙ, Sₙ

Answer 3

T₁ = first term, T₂ = second term, …, Tₙ = nᵗʰ term / n term number

Sₙ = Sum of n terms

Question 4

To find nᵗʰ term, Tₙ (in GP) =

Answer 4

ar⁽ⁿ⁻¹⁾

Question 5

How to find r, ie. Common ratio in GP

Answer 5

r = t₂/t₁

Question 6

To find nᵗʰ term, Tₙ (in HP) =

Answer 6

1 ÷ a+(n-1)d

Question 7

AP series structure

Answer 7

AP - Arithmetic Progression

a, a + d, a + 2d, a + 3d, a + 4d, …, a + (n-1)d

a = first term
d = common difference
Each next term is obtained by adding d to the previous term

Increasing order example
2, 5, 8, 11, 14, …
d = 3
Decreasing order example
52, 45, 38, 31, 24, …
d = 7

Question 8

GP series structure

Answer 8

GP - Geometric Progression

a, ar, ar², ar³, ar⁴, …, ar ⁿ⁻¹

a = first term
r = common ratio
Each next term is obtained by multiplying the previous term by r

Increasing order example = 3, 6, 12, 24, 48, …
r = 2

Question 9

HP series structure

Answer 9

HP - Harmonic Progression

It is reciprocals of the terms form an Arithmetic Progression (AP).

1 ÷ a, 1 ÷ a+d, 1 ÷ a+2d, 1 ÷ a+3d, 1 ÷ a+4d, …

If AP will be,
2, 4, 6, 8, …
a = 2, d = 2

Then HP be,
½, ¼, ⅙, ⅛, …
first term = 1/2
common difference = 1/2

Question 10

Important property of HP

Answer 10

For three numbers a, b, c in HP:

b = 2ac / a+c

This means the middle term is the harmonic mean of the other two.

Question 11

Reciprocals of AP is

Answer 11

HP

Question 12

Sum of n, Sₙ =

Answer 12

n / 2 [1ˢᵗ term + last term]
or
n / 2 [2a + (n-1) d]
or
No. of terms x Average

Question 13

No of terms =

Answer 13

(Last term - 1ˢᵗ term / Common difference) + 1

Question 14

Average =
[basic condition]

Answer 14

(1ˢᵗ term + last term) / 2
[only when there are common differences in the given set of numbers]

Question 15

When n and Average is given, then ___ needs to be find.

Answer 15

Sum of n terms

Question 16

In AP series structure, each next term is obtained by ___

Answer 16

Adding d to the previous term.

Question 17

In GP series structure, each next term is obtained by ___

Answer 17

Multiplying the previous term by r.

Question 18

Adding d to the previous term to obtain the next term is done in which series of Sequence or Progression.

Answer 18

AP

Question 19

Multiplying the previous term by r to obtain the next term is done in which series of Sequence or Progression.

Answer 19

GP

Question 20

HP is Reciprocals of

Answer 20

AP