Arithmetic Progression

Q.

If $(k-3),(2k+1),(4k+3)$ are three consecutive terms of an $AP$ . Find the value of $k$.

Q.

Find the sum of first $51$ terms of an AP whose second and third terms are $14$ and $18$ respectively.

Q. Prove that ∑1/\sqrt n+\sqrt{n+1}=\sqrt{n+1}-1, where n is positive integer.

Q. 4\sqrt3 + \sqrt{129-72\sqrt3

Q. Common difference of the AP 1, 3, 5... is 2.

1. False
2. True

Q.

The quadratic equation, whose roots are ${\sin }^{2}18°$ and ${\cos }^{2}36°$, is

1. $16x^2–12x+1=0$

2. $16x^2+12x+1=0$

3. $16x^2–12x–1=0$

4. $16x^2+10x+1=0$

Q. If the sum of a number and its square is 6/25 , then the number is [1] 1/8 [2] 1/4 [3] 1/5 [4] 1/16

Q.

If $a_1,a_2,a_3.....a_n$ are in A.P. Where $a_i>0$ for all i, then the value of
$\frac{1}{\sqrt{a_1}+\sqrt{a_2}}+\frac{1}{\sqrt{a_2}+\sqrt{a_3}}+.........+\frac{1}{\sqrt{a_{n-1}}+\sqrt{a_n}}=$

1. 
2. 
3. 
4. 

Q. What is the sum of the next two terms of the series 5, 9, 13, 17.....?

1. 50
2. 54
3. 46
4. 21

Q. The common difference of the AP 12, 6, 0, -6, -12, -18... is _____.

1. -10
2. 6
3. -6
4. 10

Q. find the value o \sqrt[3]{25/16} +\sqrt[3]{49/16} +\sqrt[3]{35/16}

Q.

If log 5 = x, find the value of log 625.

1. x/4

2. 4x

3. 3x

4. 5x

Q. The common difference in the given AP: 1, 5, 9, 13, 17, .. is _____ .

1. 2
2. 5
3. 3
4. 4

Q. Suppose that all the terms of an arithmetic progression are natural numbers. If the ratio of the sum of the first seven terms to the sum of the first eleven terms is 6 : 11 and the seventh term lies in between 130 and 140, then the common difference of this AP is___

Q. Given an A.P. of common difference 6 and sum of n terms of the A.P. is given as $a{n}^2+bn$ where a and b are constants. Find the value of 'a'.

1. 6
2. 12
3. 8
4. 3

Q. If $a^2,b^2,c^2$ are in A.P. consider two statements
(i) $\frac{1}{b+c},\frac{1}{c+a},\frac{1}{a+b}$ are in A.P.
(ii) $\frac{a}{b+c},\frac{b}{c+a},\frac{c}{a+b}$ are in A.P.

1. (i) and (ii) both incorrect
2. (i) and (ii) both incorrect
3. (i) and (ii) both correct
4. (i) incorrect (ii) correct

Q. The common difference in the given AP: 1, 5, 9, 13, 17, .. is _____ .

1. 2
2. 5
3. 3
4. 4

Q. If $\frac{3a+7b}{3a-7b}=\frac{4}{3}$ then find the value of the ratio $\frac{3a^2-7b^2}{3a^2+7b^2}$

Q.

Which of the following sequences are APs?

(i) 2, 4, 8, 16……..

(ii) 2, 3, 5, 7, 11……..

(iii) -1, -1.25, -1.5, -1.75…….

(iv) 1, -1, -3, -5, -7…………

1. (iii) and (iv)

2. (ii) and (iv)

3. (i) and (iv)

4. (i), (iii) and (iv)

Q.

if a not=0 and a-1/a=3 find

(i) a2+1/a2

(ii) a3-1/a3

Q. A simple surd has ______ term(s).

1. zero
2. one
3. two
4. three

Q. Let $a_1,a_2,a_3\cdots$ be terms of A.P.
$If\frac{a_1+a_2+\cdots a_p}{a_1+a_2+\cdots +a_q}=\frac{p^2}{q^2},p\ne q,$then $\frac{a_6}{a_{21}}$ equal

1. $\frac{41}{11}$
2. $\frac{11}{41}$
3. $\frac{7}{2}$
4. $\frac{2}{7}$

Q. $\frac{5+2\sqrt{3}}{7+4\sqrt{3}}$ = a + b$\sqrt{3}$ then find the value of a and b.

Q. For any three positive real numbers a, b and c, if $9(25a^2+b^2)+25(c^2-3ac)=15b(3a+c)$, then

1. b, c and a are in A.P
2. b, c and a are in G.P
3. a, b, and c are in A.P
4. a, b and c are in G.P

Q. Arrange the following in a meaningful order 1) Family 2) Community 3) Member 4) State 5) Country

1. $3,1,2,4,5$
2. $3,1,2,5,4$
3. $3,1,4,2,5$
4. $3,1,4,5,2$

Q.

Which of the following is true in the case of an arithmetic progression?

1. The sum of any two consecutive terms of the series is to be constant.

2. The ratio of any two consecutive terms of the series is to be constant.

3. The difference between any two consecutive terms of the series is to be constant.

4. The product of any two consecutive numbers of the series is to be constant.

Q.

What is the formula for the n th term of an A.P.?

1. a + (3n-1)d

2. a + (n-1)d

3. a + (n+1)d

4. 2a + (n-1)d

Q. If $a$ is the $A.M$ of two numbers $b$ and $c$ and $G_1,G_2$ are two Geometric means between $b$ and $c$, then the value of $G_1^3+G_2^3$

1. $3abc$
2. $2abc$
3. None of these
4. $4abc$

Q.

Suppose $a,b,c$ are in A.P. and $a^2,b^2,c^2$ are in G.P.. If $a<b<c$ and $a+b+c=\frac{3}{2}$ , then value of a is

1. 
2. 
3. 
4. 

Q.

Which of the following conditions can be used to verify that p, q, r, s are in an arithmetic progression?

1. q - p = s - r

2. p + q + r + s = 0

3. p - q = s - r

4. p + q = r + s