Relation between Terms, Their Position and Common Difference

Q.

Which term of the AP : 3, 8, 13, 18, . . . , is 78?

1. ${16}^{th}$
2. ${15}^{th}$
3. ${17}^{th}$

Q.

_____th term of the AP 3, 8, 13, 18, . . . , is 78.

Q.

${30}^{th}$ term of the AP: 10, 7, 4, ..., is

1. 97

2. 77

3. -77

4. -87

Q.

How many two-digit natural numbers are divisible by $7$?

Q.

Find the number of terms in each of the following APs:
(i)$7,13,\mathrm{19....},205$
(ii) $18,\frac{31}{2},13,...-47$

1. 34, 27

2. 26, 35

3. 27, 34

4. 35, 26

Q. If 8 times the $8^{\text{th}}$ term of an AP is equal to 15 times the ${15}^{\text{th}}$ term of the AP, then the ${23}^{\text{rd}}$ term of the AP is ___.

1. 8
2. 1
3. 0
4. 144

Q.

The number of common terms of the sequence $17,21,25,.....,417$ and $16,21,26,.......,466$ is

1. $21$

2. $19$

3. $20$

4. None of these

Q.

Find the sums given below:
(i) 7+$\frac{21}{2}$ +14+...+84
(ii) 34+32+30+...+10
(iii) -5 + (-8) + (-11) + .... + (-230)

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. If the first term of an AP is 3 and the common difference is 5, then what is the $n^{th}$ term of the AP?

1. $5n+2$
2. $3n+4$
   
3. $3n-4$
   
4. $5n-2$

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

Q.

The ${11}^{th}and{13}^{th}$ terms of an AP are 35 and 41 respectively, its common difference is:

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

Q.

Question 4 (v)
Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.
(v) $3,3+\sqrt{2},3+2\sqrt{2},3+3\sqrt{2}$

Q.

The 20th term of an arithmetic sequence is 80 and its 21st term is 84. then difference between any two terms could be

1. 18

2. 24

3. 26

4. 22

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.

Which term of the AP : 3, 8, 13, 18, . . . , is 78?

___${}^{\text{th}}$

Q. Which term of the AP : $3,15,27,39,..$. will be $132$ more than its ${54}^{th}$ term.

Q.

The first term and ${15}^{th}$ term of an AP are 7 and 35 respectively. Find the common difference.

1. 2

2. -2

3. 3

4. 2.5

Q. Question 2 (iii)
Verify that each of the following is an AP and then write its next three terms.
$\sqrt{3},2\sqrt{3},3\sqrt{3},\cdots$

Q.

In an AP
(i) given a=5, d=3, $a_n$=50, find n and $S_n$.
(ii) given $a_{12}$=37, d=3, find a and $S_{12}$.
(iii) given d=5, $S_9$=75, find a and $a_9$.
(iv) given a=8, $a_n$=62, $S_n$=210, find n and d.
(v) given l=28, S=144, and there are total of 9 terms. Find a.

Q.

If $m$ times the $m^{th}$term is equal to $n$times the $n^{th}$term of an A.P. Prove that ${(m+n)}^{th}$term of A.P. is zero

Q. What is the sum of the first 24 terms of the AP $a_1,a_2,a_3,\dots \dots$, if it is known that $a_1+a_5+a_{10}+a_{15}+a_{20}+a_{24}=225$? [4 MARKS]

Q. is not an arithmetic progression.

1. -30, -25, -20, -15, -10
2. 17, 34, 51, 68, 85, 102
3. 19, 38, 57, 75, 95, 114

Q.

Which term of the AP : 3, 8, 13, 18, . . . . is 78?

___

Q.

Find the number of terms in each of the following A.P.

$7,13,19,\dots ,205$

Q.

Which of the following are APs? If they form an A.P. find the common difference $d$ and write three more terms.

(v) $3,3+\sqrt{2},3+2\surd 2,3+3\sqrt{2}$.

Q. Which of the following sequence is not in arithmetic progression?

1. -30, -25, -20, -15, -10, -5
2. 17, 34, 51, 68, 85, 102
3. 19, 38, 57, 75, 95, 114
4. 0.2, 0.4, 0.6, 0.8, 1, 1.2

Q. If the first term of an AP is 3 and the common difference is 5, what is the $n^{th}$ term of the AP?

1. $5n+2$
   
   
2. $3n+4$
   
3. $3n-4$
   
4. $5n-2$

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 number of terms in each of the following APs respectively:

$\left(i\right)7,13,\mathrm{19....},205$
$\left(ii\right)18,\frac{31}{2},13,...-47$