Arithmetic Progression

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

2. (i) and (iv)

3. (ii) and (iv)

4. (iii) and (iv)

Q.

With 200 roses, a person starts walking from his home to the temple which is 50 m far from his home. After walking each metre, he drops 2 roses. Form a series for the number of roses the person has after walking each metre.

1. 200, 150, 100, 50, ...

2. 200, 198, 196, 194, 192, ...

3. 200, 190, 180, 170, ...

4. 200, 195, 190, 185, 180, …

Q.

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

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

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

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

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

Q. If $(a-b{)}^2,(a^2+b^2)$ are the first two terms of an AP, then which of the following will be the next term?

1. - 2ab
2. $-(a+b{)}^2$
3. 2ab
4. $(a+b{)}^2$

Q. The number of terms between 1 to 1000 divisible by 7 are ___.

1. 142
2. 144
3. 143
4. 141

Q.

Sandeep deposited Rs. 5000 in his saving account. His amount increases by 1/10 times of itself after every two years. What are the maturity amounts (in Rs.) of investment after $2^{nd}$, $4^{th}$, $6^{th}$ and $8^{th}$ years respectively? Are the maturity amounts (in Rs.) after $2^{nd}$, $4^{th}$, $6^{th}$ and $8^{th}$ years the terms of an AP?

1. 5000, 6000, 7000, 8000, Yes

2. 500, 1000, 1500, 2000, Yes

3. 5500, 6000, 6500, 7000, No

4. 5500, 6050, 6655, 7320.5, No

Q.

Find the common difference (d) in the following APs respectively.

(i) 20, 40, 60, 80, 100, ..

(ii) 5, 0, -5, -10, -15, ...

(iii) 2, 2, 2, 2, 2..

1. -20, 5, 0

2. -20, -5, 0

3. 20, 5, 0

4. 20, -5, 0

Q.

Which number comes next in the Arithmetic progression: 4, 8, 12, 16, ...?

1. 20

2. 16

3. 24

4. 12

Q.

If $x+1,3x$ and $4x+2$ are the first three terms of an AP, then its $5^{\text{th}}$ term is ___.

1. 19

2. 24

3. 14

4. 28

Q.

Does the sequence of odd numbers form an AP?

1. No

2. Yes, with a common difference of 1.

3. Yes, with a common difference of -1.

4. Yes, with a common difference of 2.