1. In an AP, if d = –4, n = 7, a_n = 4, then a is

(A) 6                                                   

(B) 7

(C) 20                                                 

(D) 28

Answer:  (D)

Explanation:

For an A.P

a_n = a + (n – 1)d

4 = a + (7 – 1)( −4)

4 = a + 6(−4)

4 + 24 = a

a = 28

2. In an AP, if a = 3.5, d = 0, n = 101, then a_n will be

(A) 0                                       

(B) 3.5

(C) 103.5                                

(D) 104.5

Answer: (B)

Explanation:

For an A.P

a_n = a + (n – 1)d

    = 3.5 + (101 – 1) × 0

    = 3.5

3. The first four terms of an AP, whose first term is –2 and the common difference is –2, are

(A) – 2, 0, 2, 4

(B) – 2, 4, – 8, 16

(C) – 2, – 4, – 6, – 8

(D) – 2, – 4, – 8, –16

Answer:  (C)

Explanation:

Let the first four terms of an A.P are a, a+d, a+2d and a+3d

Given that the first termis −2 and difference is also −2, then the A.P would be:

– 2, (–2–2), [–2 + 2 (–2)], [–2 + 3(–2)]

= –2, –4, –6, –8

4. The famous mathematician associated with finding the sum of the first 100 natural numbers is

(A) Pythagoras                                               

(B) Newton

(C) Gauss                                                       

(D) Euclid

Answer:  (C)

Explanation:

Gauss is the famous mathematician associated with finding the sum of the first 100 natural Numbers.

(A) –20                                               

(B) 20

(C) –30                                               

(D) 30

Answer:  (B)

Explanation:

6. The 21st term of the AP whose first two terms are –3 and 4 is

(A) 17                                                 

(B) 137

(C) 143                                               

(D) –143

Answer:  (B)

Explanation:

First two terms are –3 and 4

Therefore,

a = −3

a + d = 4

⇒ d = 4 − a

⇒ d = 4 + 3

⇒ d = 7

Thus,

a₂₁ = a + (21 – 1)d

a₂₁ = –3 + (20)7

a₂₁ = 137

7. If the 2nd term of an AP is 13 and the 5th term is 25, what is its 7th term?

(A) 30                                                             

(B) 33

(C) 37                                                             

(D) 38

Answer:  (B)

Explanation:

Since

a₂ = 13

a₅ = 25

⇒ a + d = 13              ….(i)

⇒ a + 4d = 25           ….(ii)

Solving equations (i) and (ii), we get:

a = 9; d = 4

Therefore,

a₇ = 9 + 6 × 4

a₇ = 9 + 24

a₇ = 33

8. If the common difference of an AP is 5, then what is a₁₈ – a₁₃?

(A) 5                                       

(B) 20

(C) 25                                     

(D) 30

Answer:  (C)

Explanation:

Since, d = 5

a₁₈ – a₁₃ = a + 17d – a – 12d

                    = 5d

                    = 5 × 5

                    = 25

9. The sum of first 16 terms of the AP: 10, 6, 2,… is

(A) –320                                             

(B) 320

(C) –352                                             

(D) –400

Answer:  (A)

Given A.P. is 10, 6, 2,…

10. The sum of first five multiples of 3 is

(A) 45                                                 

(B) 55

(C) 65                                                 

(D) 75

Answer:  (A)

Explanation:

The first five multiples of 3 are 3, 6, 9, 12 and 15

11. The middle most term (s) of the AP:–11, –7, –3, …, 49 is:

(A) 18, 20                                           

(B) 19, 23

(C) 17, 21                                           

(D) 23, 25

Answer:  (C)

Explanation:

Here, a = −11

d = − 7 – (−11) = 4

And a_n = 49

We have,

a_n = a + (n – 1)d

⇒ 49 = −11 + (n – 1)4

⇒ 60 = (n – 1)4

⇒ n = 16

As n is an even number, there will be two middle terms which are16/2th and [(16/2)+1]th, i.e. the 8th term and the 9th term.

a₈ = a + 7d = – 11 + 7 × 4 = 17

a₉ = a + 8d = – 11 + 8 × 4 = 21

12. Two APs have the same common difference. The first term of one of these is –1 and that of the other is – 8. Then the difference between their 4th terms is

(A) –1                                                 

(B) – 8

(C) 7                                                   

(D) –9

Answer:  (C)

Explanation:

The 4th term of first series is

a₄ = a₁ + 3d

The 4th term of another series is

a`₄ = a₂ + 3d

Now,

As, a₁ = –1, a₂ = –8

Therefore,

a₄ – a`₄ = (–1 + 3d) – (–8 + 3d)

a₄ – a`₄ = 7

13. If 7 times the 7th term of an AP is equal to 11 times its 11th term, then its 18th term will be

(A) 7                                                               

(B) 11

(C) 18                                                             

(D) 0

Answer:  (D)

Explanation:

According to question

   7(a + 6d) = 11(a + 10d)

⇒ 7a + 42d = 11a + 110d

⇒ 4a + 68d = 0

⇒ 4(a + 17d) = 0

⇒ a + 17d = 0

Therefore,

a₁₈ = a + 17d

a₁₈ = 0

14. In an AP if a = 1, a_n = 20 and S_n = 399, then n is

(A) 19                                                 

(B) 21

(C) 38                                                 

(D) 42

Answer:  (C)

Explanation:

15. If the numbers n – 2, 4n – 1 and 5n +2 are in AP, then the value of n is:

(A) 1                                                   

(B) 2

(C) − 1                                                

(D) − 2

Answer:  (A)

Explanation:

Let

a = n – 2

b = 4n – 1

c = 5n + 2

Since the terms are in A.P,

Therefore,

2b = a + c

⇒ 2 (4n – 1) = n – 2 + 5n + 2

⇒ 8n – 2 = 6n

⇒ 2n = 2

⇒ n = 1

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