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# Tips And Tricks And Shortcuts On AP GP And HP

Tips and Tricks for AP, GP & HP

Here, are quick and easy tips and tricks for you to solve AP, GP, and HP questions quickly, easily, and efficiently in competitive exams.

### AP

1. nth term of an AP = tn= a + (n – 1)d
2. Number of terms of an AP = n= [(l-a)/d] + 1
3. Sum of first n terms in an AP = Sn = n/2 [2a + (n − 1) d] OR  n/2  (a+l)

### GP

1. nth term of an GP =  an= a1rn-1
2. Sum of first n terms in an GP = Sn =[a1(rn – 1)/ (r-1)]

### HP

1. nth term of an HP = tn= 1/a + (n – 1)d ## Type 1: AP questions

### Question 1.

Find 10th term in the series 2, 5, 8, 11, 14……

Options:

1. 26
2. 29
3. 32
4. 27

#### Solution:

We know that,

tn = a + (n – 1)d
In the given series,

a = 2
d = 3 …. (5 – 2, 8 – 5…..)

Therefore, 10th term = t10 = a + (n-1) d

t10 = 2 + (10 – 1) * 3

t10 = 2 + 9 * 3

t10 = 29

## Type 2: GP question

### Question 1.

Find the number of terms in the series 5, 10, 20, . . ..320?

Options:

1. 5
2. 4
3. 6
4. 7

We know that,

an= a1rn-1

a = 5
r = 2

an= 320
320 = 5*2n-1

64 = 2n-1

2^6 = 2n-1

n-1 = 6

n = 7

## Type 3: HP questions

### Question 1.

Find the 15th term in the series 1/3, 1/6, 1/9, 1/12…….

Options:

1. 45
2. 1/70
3. 1/45
4. 70

#### Solution:

We know that,

tn = 1/a + (n – 1)d

Convert the HP series in AP

We get 3, 6, 9, 12……
In the given series,

a = 3

d = 3…..(6 – 3)

Therefore, 15th term = a15 =  a + (n-1) d

a15 = 3 + (15– 1) 3

a15 = 3 + 14 * 3

a15 = 3 + 42

a15 = 45

t15 = 1/45

### 2 comments on “Tips And Tricks And Shortcuts On AP GP And HP”

• Nikhil Kumar

where is the ap,gp,hp question ans video. 2
• PrepInsta

It is only available in our Online Classes. 1