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.

2839

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

$-1.2,-3.2,-5.2, \ldots \ldots$

$2,5,7,9, \ldots \ldots$

$1,2^{2}, 3^{2}, 4^{2}, \ldots \ldots$

None of these

2846

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

-4

-6

2841

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

-38

None of these

2854

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

14.9

16.0

17.1

$\mathbf{1 8 . 2}$

2856

5. The $11^{\text {th }}$ term of the A.P. $13,15 \frac{1}{2}, 18,20 \frac{1}{2}, \ldots .$. is:

$40 \frac{1}{2}$

$45 \frac{1}{2}$

2855

6. If $3^{\text {rd }}$ term of an A.P. is 4 and $9^{\text {th }}$ term is -8 , then its common difference is:

-2

-8

2844

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

-47

2845

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

-2

-3

2852

9. If $3^{\text {rd }}$ term of an A.P. is 5 and $7^{\text {th }}$ term is 13 , then its common difference is:

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:

2858

11. $15^{\text {th }}$ term of the A.P. $5,6 \frac{1}{2}, 8,9 \frac{1}{2}, \ldots . .$. is:

$15 \frac{1}{2}$

$14 \frac{1}{2}$

$27 \frac{1}{2}$

2857

12. If $11^{\text {th }}$ term of an A.P. is 38 and $16^{\text {th }}$ term is 73 , then its first term is:

-32

-35

2853

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

$\frac{61}{3}$

2848

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

$\frac{3}{4}$

$\frac{4}{3}$

$\frac{1}{4}$

$\frac{2}{9}$

2843

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

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

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

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

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

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 :
$$ \mathrm{S}=\frac{n}{2}(a+l)
$$