Sasi Math (Revised for 1024)

Scroll:Sequences and series >> Arithmetric Progressions >> saq (4223)

Written Instructions:

For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..

For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.

Leave your answers in the simplest form or correct to two decimal places.

How many terms are there in the following Arrithmetic Progression

19, 22, 25.....160

Difference =

n =

Answer:_______________

How many terms are there in the following Arrithmetic Progression

19, 21, 23.....61

Difference =

n =

Answer:_______________

How many terms are there in the following Arrithmetic Progression

7, 11, 15.....99

Difference =

n =

Answer:_______________

How many terms are there in the following Arrithmetic Progression

12, 14, 16.....56

Difference =

n =

Answer:_______________

How many terms are there in the following Arrithmetic Progression

10, 12, 14.....82

Difference =

n =

Answer:_______________

How many terms are there in the following Arrithmetic Progression

20, 25, 30.....195

Difference =

n =

Answer:_______________

How many terms are there in the following Arrithmetic Progression

16, 19, 22.....94

Difference =

n =

Answer:_______________

How many terms are there in the following Arrithmetic Progression

11, 16, 21.....156

Difference =

n =

Answer:_______________

How many terms are there in the following Arrithmetic Progression

18, 20, 22.....84

Difference =

n =

Answer:_______________

10)

How many terms are there in the following Arrithmetic Progression

20, 22, 24.....114

Difference =

n =

Answer:_______________

How many terms are there in the following Arrithmetic Progression

19, 22, 25.....160

Difference = Answer: 3

n = Answer: 48

SOLUTION 1 :

Given A.P. is 19,22,25.....160

Here a = 19

d = 22 - 19

d = 3

t_n = a + (n-1)d

t_n = 160

a + (n-1)d = 160

t₄₈ = 19 + (n-1)3 = 160

= 19 + (3n- 3) = 160

= 3n + 16 = 160

= 3n = 160-16

3n = 144

n = $\frac{144}{3}$ = 48

How many terms are there in the following Arrithmetic Progression

19, 21, 23.....61

Difference = Answer: 2

n = Answer: 22

SOLUTION 1 :

Given A.P. is 19,21,23.....61

Here a = 19

d = 21 - 19

d = 2

t_n = a + (n-1)d

t_n = 61

a + (n-1)d = 61

t₂₂ = 19 + (n-1)2 = 61

= 19 + (2n- 2) = 61

= 2n + 17 = 61

= 2n = 61-17

2n = 44

n = $\frac{44}{2}$ = 22

How many terms are there in the following Arrithmetic Progression

7, 11, 15.....99

Difference = Answer: 4

n = Answer: 24

SOLUTION 1 :

Given A.P. is 7,11,15.....99

Here a = 7

d = 11 - 7

d = 4

t_n = a + (n-1)d

t_n = 99

a + (n-1)d = 99

t₂₄ = 7 + (n-1)4 = 99

= 7 + (4n- 4) = 99

= 4n + 3 = 99

= 4n = 99-3

4n = 96

n = $\frac{96}{4}$ = 24

How many terms are there in the following Arrithmetic Progression

12, 14, 16.....56

Difference = Answer: 2

n = Answer: 23

SOLUTION 1 :

Given A.P. is 12,14,16.....56

Here a = 12

d = 14 - 12

d = 2

t_n = a + (n-1)d

t_n = 56

a + (n-1)d = 56

t₂₃ = 12 + (n-1)2 = 56

= 12 + (2n- 2) = 56

= 2n + 10 = 56

= 2n = 56-10

2n = 46

n = $\frac{46}{2}$ = 23

How many terms are there in the following Arrithmetic Progression

10, 12, 14.....82

Difference = Answer: 2

n = Answer: 37

SOLUTION 1 :

Given A.P. is 10,12,14.....82

Here a = 10

d = 12 - 10

d = 2

t_n = a + (n-1)d

t_n = 82

a + (n-1)d = 82

t₃₇ = 10 + (n-1)2 = 82

= 10 + (2n- 2) = 82

= 2n + 8 = 82

= 2n = 82-8

2n = 74

n = $\frac{74}{2}$ = 37

How many terms are there in the following Arrithmetic Progression

20, 25, 30.....195

Difference = Answer: 5

n = Answer: 36

SOLUTION 1 :

Given A.P. is 20,25,30.....195

Here a = 20

d = 25 - 20

d = 5

t_n = a + (n-1)d

t_n = 195

a + (n-1)d = 195

t₃₆ = 20 + (n-1)5 = 195

= 20 + (5n- 5) = 195

= 5n + 15 = 195

= 5n = 195-15

5n = 180

n = $\frac{180}{5}$ = 36

How many terms are there in the following Arrithmetic Progression

16, 19, 22.....94

Difference = Answer: 3

n = Answer: 27

SOLUTION 1 :

Given A.P. is 16,19,22.....94

Here a = 16

d = 19 - 16

d = 3

t_n = a + (n-1)d

t_n = 94

a + (n-1)d = 94

t₂₇ = 16 + (n-1)3 = 94

= 16 + (3n- 3) = 94

= 3n + 13 = 94

= 3n = 94-13

3n = 81

n = $\frac{81}{3}$ = 27

How many terms are there in the following Arrithmetic Progression

11, 16, 21.....156

Difference = Answer: 5

n = Answer: 30

SOLUTION 1 :

Given A.P. is 11,16,21.....156

Here a = 11

d = 16 - 11

d = 5

t_n = a + (n-1)d

t_n = 156

a + (n-1)d = 156

t₃₀ = 11 + (n-1)5 = 156

= 11 + (5n- 5) = 156

= 5n + 6 = 156

= 5n = 156-6

5n = 150

n = $\frac{150}{5}$ = 30

How many terms are there in the following Arrithmetic Progression

18, 20, 22.....84

Difference = Answer: 2

n = Answer: 34

SOLUTION 1 :

Given A.P. is 18,20,22.....84

Here a = 18

d = 20 - 18

d = 2

t_n = a + (n-1)d

t_n = 84

a + (n-1)d = 84

t₃₄ = 18 + (n-1)2 = 84

= 18 + (2n- 2) = 84

= 2n + 16 = 84

= 2n = 84-16

2n = 68

n = $\frac{68}{2}$ = 34

10)

How many terms are there in the following Arrithmetic Progression

20, 22, 24.....114

Difference = Answer: 2

n = Answer: 48

SOLUTION 1 :

Given A.P. is 20,22,24.....114

Here a = 20

d = 22 - 20

d = 2

t_n = a + (n-1)d

t_n = 114

a + (n-1)d = 114

t₄₈ = 20 + (n-1)2 = 114

= 20 + (2n- 2) = 114

= 2n + 18 = 114

= 2n = 114-18

2n = 96

n = $\frac{96}{2}$ = 48