Common Difference

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

1. $3$
2. $3+\sqrt{2}$
3. $\sqrt{2}$
4. $2\sqrt{2}$

Q. If the ${11}^{\text{th}}$ and${13}^{\text{th}}$ terms of an AP are 35 and 41 respectively, then its common difference is ___.

1. 38
2. 32
3. 6
4. 3

Q.

If 2x, x + 10, 3x + 2 are in AP. Find the value of x.

__

Q.

In the arithmetic progression given below, find the common difference.
1, a, b, c, 9

1. 0

2. 3

3. 1

4. 2

Q.

Which of the following list of numbers forms an AP?
(i) 4, 4 + $\sqrt{3}$ , 4 + 2$\sqrt{3}$, 4 + 3$\sqrt{3}$, 4 + 4$\sqrt{3}$

(ii) 0.3, 0.33, 0.333, 0.3333, 0.33333

(iii) $\frac{3}{5}$, $\frac{6}{5}$ , $\frac{9}{5}$ , $\frac{12}{5}$ , 3

(iv) -$\frac{1}{5}$ , -$\frac{1}{5}$ , -$\frac{1}{5}$ , -$\frac{1}{5}$ , -$\frac{1}{5}$

1. Only (i) and (ii)

2. Only (iii) and (iv)

3. Only (ii) and (iii)

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

Q.

Which of the following series forms an AP?

$\left(i\right)a–2d,a–d,a,a+d,a+2d$

$\left(ii\right)a,a+d,a+2d,a+3d,a+4d$

$\left(iii\right)a–3d,a–d,a+d,a+3d$

1. $\left(i\right)and\left(ii\right)$

2. $\left(i\right)and\left(iii\right)$

3. $\left(i\right),\left(ii\right)and\left(iii\right)$

4. $\left(ii\right)and\left(iii\right)$

Q.

If the first term of an AP is 4 and the common difference is -4, find the second term.

1. 0

2. 8

3. -16

4. -4

Q. The sequence of numbers 5, - 2, -9, -16, ...is

1. an AP with common difference -7.
2. not an AP.
3. an AP with common difference 7.
4. an AP with common difference 3.

Q.

The sides of a right triangle are in an AP. The area and the perimeter of the triangle are numerically equal. Find its perimeter.

1. 24 units

2. 34 units

3. 44 units

4. Can’t say, the common difference should be given

Q.

The sum of 3 consecutive terms of an A.P = 33 and the sum of their squares is equal to 371. Then the terms are 9, 11, 13 or 13, 11, 9.

1. True

2. False