Suresh Lecturer

MCQ Quiz for 10th Maths

Chapter 5 Arithmetic Progression

Class 10 Mathematics Chapter 5 Arithmetic Progression AP Multiple Choice Questins Quiz / MCQ Quiz online test base on NCERT useful for NTSE Maths Olympiad Board Exam Important Questions.

2838

1. Which one is an A.P. series?

$1,2,4,8, \ldots \ldots$

$5,8,12,15, \ldots \ldots$

$3,6,9,12, \ldots \ldots$..

None of these

2845

2. The common difference of A.P. $3,1,-1,-3, \ldots .$. is:

-2

-3

2858

3. $15^{\text {th }}$ term of the A.P. $5,6 \frac{1}{2}, 8,9 \frac{1}{2}, \ldots . .$. is:

$15 \frac{1}{2}$

$14 \frac{1}{2}$

$27 \frac{1}{2}$

2846

4. The common difference of A.P.: $-5,-1,3,7, \ldots .$. is:

-4

-6

2853

5. $15^{\text {th }}$ term of A.P. $\frac{1}{3}, \frac{5}{3}, \frac{9}{3}, \frac{13}{3}, \ldots . .$. is:

$\frac{61}{3}$

2837

6. $12^{\text {th }}$ term of the A.P.: $7,10,13,16, \ldots .$. is:

2847

7. $10^{\text {th }}$ term of an A.P. : $2,7,12, \ldots .$. is:

None of these

2843

8. Which one is an A.P. series?

$a, a^{2}, a^{3}, \ldots$

$1^{2}, 3^{2}, 5^{2}, 7^{2}, \ldots$

$a, 2 a, 3 a, 4 a, \ldots$

$1,3,9,27, \ldots$

2841

9. $11^{\text {th }}$ term of the A.P. $-3,-\frac{1}{2}, 2 \ldots .$. is:

-38

None of these

2859

10. If the third term of an A.P. is 12 and $10^{\text {th }}$ term is 26 , then its $20^{\text {th }}$ term is:

2848

11. The common difference of the A.P., $\frac{1}{3}, \frac{5}{3}, \frac{9}{3} \ldots \ldots$. is:

$\frac{3}{4}$

$\frac{4}{3}$

$\frac{1}{4}$

$\frac{2}{9}$

2844

12. In an A.P.: $2,7,12, \ldots, 20^{\text {th }}$ term is:

-47

2849

13. The $10^{\text {th }}$ term of the A.P.: $-0.1,-0.2,-0.3, \ldots . .$. is:

-0.9

-0.8

-0.1

-1.1

2854

14. The $14^{\text {th }}$ term of A.P. $0.6,1.7,2.8,3.9$, ...... is:

14.9

16.0

17.1

$\mathbf{1 8 . 2}$

2840

15. $30^{\text {th }}$ term of the A.P. $10,7,4, \ldots . .$. is:

-77

None of these

Real Numebrs Chapter 5 AP

1. Arithmetic Progression:
An arithmetic progression (AP) is a list of numbers in which each term is obtained by adding a fixed number $d$ to the preceding term, except the first term. The fixed number $d$ is called the common difference.

2.General Form of an AP:
The general form of an AP is $a, a+d, a+2 d, a+3 d, \ldots$

3.. A given list of numbers $a_{1}, a_{2}, a_{3}, \ldots$ is an AP if the differences $a_{2}-a_{1}, a_{3}-a_{2}$, $a_{4}-a_{3}, \ldots$, give the same value, i.e., if $a_{k+1}-a_{k}$ is the same for different values of $k$.

4. General Term of an AP
In an AP with first term $a$ and common difference $d$, the $n$th term (or the general term) is given by $a_{n}=a+(n-1) d$.

5. The sum of the first $n$ terms of an AP :
$$ \mathrm{S}=\frac{n}{2}[2 a+(n-1) d]
$$
6. If $l$ is the last term of the finite AP, say the $n$th term, then the sum of all terms of the AP is given by :
$$ \mathrm{S}=\frac{n}{2}(a+l)
$$