Three and Four Terms in an AP

Q.

The $4^{th}$ term from the end of an AP is $–11,–8,–5,\dots ..,49$ is
$A.37$
$B.40$
$C.43$
$D.58$

Q. Question 27
Find the sum of first 17 terms of an AP whose $4^{th}$ and $9^{th}$ terms are – 15 and –30, respectively.

Q. If the sum of 99 terms of AP is 198, then what is the value of the 50th term? [1 MARK]

Q. The sum and product of three consecutive terms of an AP is given to be 21 and 168. If the common difference is known to be postitive, then the ${10}^{\text{th}}$ term of the AP is ___.

1. 52
2. 38
3. 45
4. 58

Q. The sum and product of three consecutive terms of an AP is given to be 6 and -90. If the common difference is known to be negative, then the ${12}^{\text{th}}$ term of the AP is ___.

1. -75
2. -68
3. 79
4. -70

Q. Question 7
Show that the sum of an AP whose first term is a, the second term b and the last term c, is equal to $\frac{(a+c)(b+c-2a)}{2(b-a)}$

Q. What is the sum of first 11 terms of an AP whose middle term is 30? [2 MARKS]

Q. If the sum of four consecutive terms of an AP is 20 and the sum of their squares is 120, then the numbers are .

1. $2,4,6,8$
2. $1,2,3,4$
3. $4,5,6,7$

Q. The sum of three consecutive terms of an $AP$ is $21$ and the sum of the squares of these terms is $165:$ Find these terms.

Q. Find four numbers in AP, whose sum is $20$ and the sum of whose squares is $120.$

1. Numbers are $3,6,9,12$
   
2. Numbers are $1,3,5,7$
   
3. Numbers are $2,4,6,8$
4. Data insufficient
   

Q.

Find the 5th term of an arithmetic sequence whose nth term is 3n - 2.

1. 13

2. 15

3. 11

4. 17

Q.

Find an arithmetic sequence whose first term is 5 and common difference is 9.

1. -9 , 14, -19, 24...

2. -5 , -14 , -23, -32....

3. 9 , 14, 19, 24...

4. 5, 14, 23, 32....

Q. Common difference of the AP 5, 3 , 1... is 2.

1. True
2. False

Q.

What is the missing number in this sequence: 12, 10, __ , 6?

1. 8

2. 9

3. 22

4. 4

Q.

If terms 9, x, 21 form an arithmetic progression, then the value of x is ____.

1. 11

2. 17

3. 13

4. 15

Q. Match the patterns with their number patterns.

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

Q. The sum of $n,2n$ and $3n$ terms of an $AP$ are $x,y,z$. Prove that $z=3(y-x)$.

Q.

Two AP's have the same common difference. The difference between their ${100}^{th}$ terms is 100, what is the difference between their ${1000}^{th}$ terms?

1. 100

2. 200

3. 150

4. 1000

Q. The sum of the first three terms of an A.P. is $9$ and the sum of their square is $35$. The sum to first $n$ terms of the series can be

1. $n(4-n)$
2. $n^2$
3. $n(n+1)$
4. $n(6-n)$

Q. Find the ${18}^{th}$ term of the A.P., $\sqrt{2},3\sqrt{2},5\sqrt{2}$.....

1. $36\sqrt{2}$
2. $35\sqrt{2}$
3. $34\sqrt{2}$
4. $33\sqrt{2}$

Q. Find the $18$th term of the AP $\sqrt{2},\sqrt{18},\sqrt{50},\sqrt{98},.....$.

Q.

Arul has 16 Apples, Raghav has 32 Apples, Ramesh has 48 Apples. The number of apples they possess forms an A.P with a common difference of

1. 32

2. 46

3. 16

4. 9