Relation between Terms, Their Position and Common Difference

Q. Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.
(i) $2,4,8,16,\dots$
(ii) $2,\frac{5}{2},3,\frac{7}{2},\dots$
(iii)$-1.2,-3.2,-5.2,-7.2\dots$
$\left[5\right]$

Q.

Find the common difference of the given AP: $\frac{3}{4},1,1\frac{1}{4}$.........

1. $\frac{1}{4}$

2. $\frac{1}{3}$

3. $\frac{1}{2}$

4. $-\frac{1}{4}$

Q. Which of the following is a term of an AP whose first term is 2 and the common difference is 4?

1. 23
2. 46
3. 69
4. 92

Q.

The digits of a positive integer whose three digits are in AP and their sum is 21. The number obtained by reversing the digits is 396 less than the original number. Find the number.

1. 795

2. 579

3. 975

4. 546

Q. If the $9^{\text{th}}$ term of an AP is 15 and the common difference is 2, then the $1^{\text{st}}$ term of the AP is ___.

1. 1
2. -1
3. 2
4. 0

Q.

The 5th term of an arithmetic sequence is 38 and the 9th term is 66. What its 10th term is

1. 93

2. 83

3. 73

4. 63

Q.

A sum of ₹ 2000 is invested at 4% simple interest per year. If the total interest at the end of each year forms an AP, then the interest at the end of the 30th year will be

1. ₹ 1200

2. ₹ 2400

3. ₹ 4800

4. ₹ 5500

Q.

13th term in an arithmetic sequence 8, 16, 24, 32, ... is

1. 108

2. 88

3. 104

4. 93

Q.

If the $t^{th}$ term of an AP is s and $s^{th}$ term of the same AP is t, then $a_n$ is

1. t + s + n

2. t + s - n

3. t - s + n

4. t - s - n

Q. An AP has the first term as 2 and the common difference as 4. Which term in the AP is the first multiple of 23 to appear in the AP?

1. ${11}^{th}term$
2. ${12}^{th}term$
3. ${14}^{th}term$
4. ${35}^{th}term$