class 10 maths Arithmetic Progressions Hots Questions

Q 1 :
In an A.P., if the first term a = 7, nth term an 84 and the sum of first n terms $S_{n}$ = 2093/2, then n is equal to:

22
24
23
26

1

2

3

4

(3)

$S_{n} = \frac{n}{2} (a + a_{n}) \Rightarrow \frac{2093}{2} = \frac{n}{2} (7 + 84)$

$\Rightarrow 91 n = 2093 \Rightarrow n = 23$

Q 2 :
Which term of the A.P. –29, –26, –23, ..., 61 is 16?

11th
16th
10th
31st

1

2

3

4

(2)

Given, $a = - 29$

$d = - 26 - (- 29) = - 26 + 29 = 3 \Rightarrow d = 3$

$a_{n} = 16$

Here we know, $a_{n} = a + (n - 1) d$

$\Rightarrow 16 = - 29 + (n - 1) 3$

$\Rightarrow 16 + 29 = (n - 1) 3 = 15$

$\Rightarrow n - 1 = \frac{45}{3} = 15$

$\Rightarrow 15 = n - 1 \Rightarrow n = 16$

Q 3 :
The 7th term from the end of the A.P. : – 8, – 5, – 2, ..., 49 is :

67
13
31
10

1

2

3

4

(3) 31

Q 4 :
If k + 7, 2k – 2 and 2k + 6 are three consecutive terms of an A.P., then the value of k is :

15
17
5
1

1

2

3

4

(2) 17

Q 5 :
The common difference of an A.P. in which a15 – a11 = 48, is

12
16
–12
–16

1

2

3

4

(1)

$a_{15} - a_{11} = 48$

$\Rightarrow a + 14 d - a - 10 d = 48$

$\Rightarrow 4 d = 48 \Rightarrow d = 12$

Topic Question Set

Q 1 :
In an A.P., if the first term a = 7, nth term an 84 and the sum of first n terms $S_{n}$ = 2093/2, then n is equal to:

Q 2 :
Which term of the A.P. –29, –26, –23, ..., 61 is 16?

Q 3 :
The 7th term from the end of the A.P. : – 8, – 5, – 2, ..., 49 is :

Q 4 :
If k + 7, 2k – 2 and 2k + 6 are three consecutive terms of an A.P., then the value of k is :

Q 5 :
The common difference of an A.P. in which a15 – a11 = 48, is

Want Us to Email you About Special Offers & Updates?

Topic Question Set

Q 1 : In an A.P., if the first term a = 7, nth term an 84 and the sum of first n terms Sn = 2093/2, then n is equal to:

Q 2 : Which term of the A.P. –29, –26, –23, ..., 61 is 16?

Q 3 : The 7th term from the end of the A.P. : – 8, – 5, – 2, ..., 49 is :

Q 4 : If k + 7, 2k – 2 and 2k + 6 are three consecutive terms of an A.P., then the value of k is :

Q 5 : The common difference of an A.P. in which a15 – a11 = 48, is

Want Us to Email you About Special Offers & Updates?

Q 1 :
In an A.P., if the first term a = 7, nth term an 84 and the sum of first n terms $S_{n}$ = 2093/2, then n is equal to:

Q 2 :
Which term of the A.P. –29, –26, –23, ..., 61 is 16?

Q 3 :
The 7th term from the end of the A.P. : – 8, – 5, – 2, ..., 49 is :

Q 4 :
If k + 7, 2k – 2 and 2k + 6 are three consecutive terms of an A.P., then the value of k is :

Q 5 :
The common difference of an A.P. in which a15 – a11 = 48, is