Common Difference

Q.

Why any number power 0 =1?

Q. 42. If a+b+c ≠ 0 , then prove that a3+b3+c3=3abc, only when a = b = c.

Q. 21 If a b c are real numbers such that ab/a+b =1/3 bc/b+c=1/4 ca/c+a=1/5 then find the valie of abc/ab+bc+ca

Q. 1.The value of the product of (x-a) (x-b) (x-c) , given that the sum a+b+c=7 , ab+bc+ca=0 and abc = -36 , is

Q.

If a and b are rational numbers, find the values of a and b in the following equality

5+2√3 ÷7+4 √3 = a + b √ 3

Q. The next term of the A.P 2, 6, 10, 14 is .

1. 16
2. 17
3. 18
4. 20

Q.

Express 0.8 + 0. 777… + 0.4343… in the form of p/q where p and q are integers and
q ≠ 0.

Q.

P(x) is equal to cx+d, c is not equal to 0, c, d are real numbers

Q. If a, m, n are positive ingegers, then ${\left\{\sqrt[m]{\sqrt[n]{a}}\right\}}^{mn}$is equal to

(a) a^mn

(b) a

(c) a<sup>m/n

(d) 1</sup>

Q. Simplify 1/✓8-3✓2

Q.

In an AP, the sum of the first ten terms is -80 and the sum of the next ten terms is -280. Find the AP.

1. -1 , -1 , 3 , 5 ...

2. 1 , 1 , 3 , -5 ...

3. 1 , -1 , -3 , -5 ...

4. -1 , -1 , -3 , 5 ...

Q. Common difference of an A.P must be a ---

1. real no.
2. Rational no.
3. None of the above
4. Positive integer

Q. If a² + b² + c² − ab − bc − ca =0, then

(a) a + b + c

(b) b + c = a

(c) c + a = b

(d) a = b = c

Q. The $n^{th}$ term of an arithmetic sequence is 15 -7n. Find the common difference of the sequence.

1. 7
2. -7
3. 6
4. 11

Q.

Find the next term in the following sequence: a-2d, a-d, a, a+d, ...

1. a - 2d

2. 2a + 2d

3. 4a + 2d

4. a + 2d

Q. If common difference = 0, the nature of the AP is said to be ________ .

1. increasing
2. decreasing
3. constant
4. variable

Q. In a quadrilateral $ABCD$, the line segments bisecting $\angle C$ and $\angle D$ meet at $E$. prove that $\angle A+\angle B=2\angle CED$

Q. b÷2-1÷4=b÷4

Q. If the sum of n terms of an A.P. is $nA+n^{2}B,$ where A, B are constants, then its common difference will be
[MNR 1977]

1. A + B
2. 2B
3. 2A
4. A - B

Q. If $a_1,a_2,a_3$ .... a_{n} are in A. P., then the common difference is--

1. $a_2-a_1$
2. $a_4-a_3$
3. $a_n-a_{n-1}$
4. $a_7-a_6$

Q. State True or False.

1. True
2. False

Q. For all positive integers n, show that ²ⁿC_n + ²ⁿC_{n − 1} = (^{2n + 2}C_{n + 1}).

Q. The $n^{th}$ term of an AP is given by $a_n=2+5n$. The sum of the first 10 terms of the AP is .

1. 295
2. 290
3. 350
4. 330

Q. If $(\frac{12}{13}{)}^4\times (\frac{13}{12}{)}^{-8}=(\frac{12}{13}{)}^{2x}$, then find the value of $x$.

Q. 4 /root 7 + root 3 .rationalise the denominator of

Q.

Find the common difference of the following arithmetic progression.
$3+2\sqrt{2},3+4\sqrt{2},3+6\sqrt{2},3+8\sqrt{2}$

1. $2\sqrt{2}$

2. $\sqrt{2}$

3. $3+\sqrt{2}$

4. $3$

Q. The common difference for the arithmetic progression
$3+2\sqrt{2},3+4\sqrt{2},3+6\sqrt{2},3+8\sqrt{2}$ is

1. $2\sqrt{2}$
2. $3$
3. $3+\sqrt{2}$

Q. If the first term of an AP is 4 and the common difference is -4, then the next term is .

1. -16
2. -4
3. 8
4. 0

Q. Find the sum of 30 terms of an A.P. whose second term is 2 and seventh term is 22.
​

Q. Find $k$ given the consecutive arithmetic terms:
$k,7,10$