Arithmetic Progressions Test

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Arithmetic Progressions Test - 2

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Question 1
1 / -0

Which of the following is the AP whose 9^th term is 101 and a₈ – a₂ = 60?

A
22, 32, 42, 52, …..

B
9, 19, 29, 39, …..

C
21, 31, 41, 51, …..

D
21, 30, 31, 40, ……

Solution

a₉ = 101
a + 8d = 101 …. (1)
Also a₈ – a₂ = 60
a₂ + 6d – a₂ = 60
6d = 60
d = 10
Putting in equation (1), we get
a + 80 = 101
a = 101 – 80
a = 21
Required AP is 21, 31, 41, 51, ……..
Question 2
1 / -0

If a + 1, 3a, 4a + 2 are in AP, then the value of a is

A
3

B
2

C
1

D
0

Solution

a + 1, 3a, 4a + 2 are in AP.
If x, y, z are in AP, then 2y = x + z.
Therefore, 2(3a) = a + 1 + 4a + 2
6a = 5a + 3
6a - 5a = 3
a = 3
Question 3
1 / -0

What would be the 19^th term of the given sequence?

1, 5, 9, 13, …

A
92

B
84

C
75

D
73

Solution

1, 5, 9, 13, …
n^th term = nd + (a – d)
19^th term = 19 × 4 + (1 – 4)
= 76 – 3 = 73
Question 4
1 / -0

Find the next term in the sequence 10, 20, 40, 70, ...

A
90

B
100

C
110

D
130

Solution

n^th term = a + (n - 1)d + (n - 1) (n - 2) c
5^th term = 10 + 4 x 10 + x 4 x 3 x 10
= 50 + 60 = 110
Question 5
1 / -0

What is the n^th term of the given sequence?

0, 2, 4, 6, …

A
1n

B
2n – 2

C
2n

D
2n + 2

Solution

Common difference sequence:
n^th term = dn + (a – d)
= 2 × n + (0 – 2)
= 2n – 2
Question 6
1 / -0

The first term of a sequence is 15 and the common difference is 7. Find its 29^th term.

A
210

B
211

C
212

D
214

Solution

a = 15, d = 7, n = 29
T₂₉ = dn + (a – d)
= 7 29 + (15 – 7)
= 211
Question 7
1 / -0

The first term of a sequence is 24 and the common difference is – 6. Find its 45^th term.

A
240

B
220

C
- 220

D
- 240

Solution

a = 24 d = – 6
45^th term will be
T₄₅ = dn + (a – d)
= – 6 45 + (24 – (– 6)
= – 270 + 30
= – 240
Question 8
1 / -0

Ruby has 36 stamps in her collection. She adds 7 stamps to her collection every month. If the pattern continues, how many stamps will she have at the end of eighth month?

A
92

B
85

C
78

D
61

Solution

8^th term = dn + (a - d)
= 7 x 8 + (36 - 7)
= 56 + 29 = 85
Number of stamps after eight months = 85 + 7 = 92
Question 9
1 / -0

The first term, last term and sum of all the terms of an AP are 12, 160 and 3268, respectively. Find the number of terms in the AP.

A
36

B
34

C
39

D
38

Solution

Here, a = 12, a_n = 160 and S_n = 3268
So, 3268 =
n = = 38
Question 10
1 / -0

Which of the following values is the sum of the first five terms of the AP: -45, -39, -33 …?

A
-258

B
-165

C
-156

D
-150

Solution

The terms are -45, -39, -33 …
Here, a = -45 and d = -39 + 45 = 6
∴ S₅ = = = = -165
Question 11
1 / -0

A display of food items on grocery shelves consists of 30 items in the bottom row, 28 items in the next row, 26 items in the next and so on. lf the topmost row has 4 items, then how many food items are there in the display?

A
248

B
238

C
258

D
228

Solution

a = 4, d = 2, = 30
S_n =
n = ?
= a + (n – 1)d
30 = 4 + (n – 1) 2
13 = n – 1
Or, n = 14
S_n =
= 238
Question 12
1 / -0

Amy read 12 pages of a book on the first day, 17 pages on the second day, and 23 pages on the third day. If the pattern continued, how many pages did she read on the fourth day?

A
30

B
33

C
35

D
40

Solution

12, 17, 23, ...
The pattern is +5, +6... and so on.
So, on the fourth day, she will read 23 + 7 = 30 pages
Question 13
1 / -0

Rosy kept 2 candies in the first box, 4 in the second box, 6 in the third box, and 8 in the fourth box. If the pattern continued, how many candies did she keep in the twelfth box?

A
20

B
22

C
24

D
26

Solution

12^th term = dn + (a – d)
= 2 × 12 + (2 – 2)
= 24 + 0
= 24
Question 14
1 / -0

Rosy works as a telephone operator. She attended 5 calls on the first day, 10 calls on the second day, 20 calls on the third day, and 40 calls on the fourth day. If the pattern continues, find the number of calls she will attend on the seventh day.

A
120

B
220

C
320

D
420

Solution

5, 10, 20, 40, ...
7^th term = ?
Each time, the previous term is being multiplied by 2.
First day: 5 x 2⁰= 5
Second day: 5 x 2¹ = 10
Third day: 5 x 2² = 20
...
...
...
Seventh day: 5 x 2⁶ = 320
So, on the seventh day, Rosy will attend 320 calls.
Question 15
1 / -0

The sum of the interior angles of a triangle is 180°, that of a quadrilateral is 360° and that of a pentagon is 540°. Assuming the pattern continues, find the sum of the interior angles of a dodecagon.

A
1600°

B
1540°

C
1800°

D
1920°

Solution

180°, 360°, 540°, _____
Number of sides of a dodecagon = 12

Sum of interior angles of dodecagon = (12 - 2) 180°
= 1800°