General Term of an AP

Q. Question 3 (viii)
In an AP:
(viii) Given $a_n=4$, d = 2, $S_n=-14$, find n and a.

Q.

Three numbers are in A.P. whose sum is $33$ and product is $792$, then the smallest number from these numbers is

1. $4$

2. $8$

3. $11$

4. $14$

Q. The sums of the first n, 2n and 3n terms of an AP are respectively denoted by x, y and z. Find the value of $\frac{z}{y-x}$ [4 MARKS]

Q.

The sum of the first 20 terms of an AP is known to be 1280, and the common difference is 20. Then the fourth term of the AP will be __.

1. -64

2. -66

3. -62

4. -60

Q.

Is 200 any term of the sequence 3, 7, 11, 15, ...?

Q.

The algebraic form of an arithmetic sequence is 4n+2. The numbers of terms required to get the sum as 880

1. -20

2. -22

3. 22

4. 20

Q.

The ${17}^{th}$ term of an AP exceeds its ${10}^{th}$ term by 7. Its common difference is ___

Q.

Question 4 (i)
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, …

Q.

The ${17}^{th}$ term of an AP exceeds its ${10}^{th}$ term by 7. Find the common difference.

___

Q.

Question 4 (ii)
Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.
(ii) $2,\frac{5}{2},3,\frac{7}{2},\dots$

Q.

The 10th term of an arithmetic sequence is 65 and its 15th term is 20. Then 20th term is

1. -9

2. 25

3. 9

4. -25

Q. A cyber cafe charges ₹20 for the first hour and then ₹10 for subsequent hours. If Ramu plays games for 4 hours, then he has to pay .

1. ₹40
2. ₹50
3. ₹100

Q.

Find the ${20}^{th}$ term from the last term of the AP: 3, 8, 13, ...., 253.

1. 164

2. 158

3. 152

4. 182

Q. If the $t^{\text{th}}$ term of an AP is $s$ and $s^{\text{th}}$ 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.

The $n^{th}$ term of an A.P is $p^2$ and the sum of the first $n$ terms is $s^2$. The first term is

1. $\frac{p^{2}n+2s^2}{n}$

2. $\frac{p^{2}n+2s^2}{n^2}$

3. $\frac{p{s}^2-p^{2}s}{n}$

4. $\frac{2s^2-p^{2}n}{n}$

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.

If the sum of the first n terms of an AP is (4n− $n^2$), what is the first term (that is $S_1$)? What is the sum of first two terms? What is the second term? Similarly, find the $3^{rd}$, the ${10}^{th}$ and the $n^{th}$ terms.

Q.

Find the sum of the positive even integers up and including $50$.

Q. Which term of the arithmetic sequence $24,23\frac{1}{4},22\frac{1}{2},21\frac{3}{4},....$ is $3$?

Q. Consider the following AP sequence:
1, a, b, c, 9.
Find the common difference.

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

Q. Match the APs to their $n^{\text{th}}$ terms.

1. $3n+2$
2. $2n-1$
3. $3n-2$
4. $6-n$

Q.

Examine that the sequence $\mathrm{7,\; 13,\; 19,\; 25,\; ...}$ is an AP. Also, find the common difference.

Q. The 10th term of an arithmetic sequence is 65 and its 15th term is 20. Find 20th term of this arithmetic sequence.

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. \N
3. -1
4. 2

Q. The fifth term of an AP is 25 and the ninth term is 41. The first term of the AP is .

1. 9
2. 3
3. 4

Q.

If $a_1,a_2,a_3,a_4$ are in AP, then

1. $a_1+a_4=a_2+a_3$
   

2. $a_1+a_2=a_2+a_3$
   

3. $a_1+a_2=a_3+a_4$
   

4. $a_1+a_3=a_2+a_4$

Q.

Aditya has $5$ exams in an academic year. His marks increase by $2\%$ based on his previous test marks. If Aditya scores $70$ in his $1$st exam, what is his score in the last academic exam?

1. 87

2. 76

3. 74

4. 77

Q. The eighth term of an AP is half its second term and the eleventh term exceeds one third of its fourth term by 1. Find the 15th term.

Q. From the following options, only can be a term of AP whose first term is 2 and the common difference is 4.

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

Q. If the $5$th term of an A.P is eight times the first term and $8$th term exceeds twice the $4$th term by $3$, then the common difference is

1. $7$
2. $5$
3. $6$
4. $3$