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
AP GP HP _Tips and tricks and Shortcuts

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

Correct option: B

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

Solution:

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

Correct Option. D

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

Correct option: C

 

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