nth Term of A.P

Q.

If $x,y,z$ are in arithmetic progression with common difference $d,x\ne 3d$, and the determinant of the matrix

$\left[\begin{array}{ccc}3& 4\sqrt{2}& x\\ 4& 5\sqrt{2}& y\\ 5& k& z\end{array}\right]=0$

is zero, then the value of $k^2$ is:

1. $6$

2. $36$

3. $72$

4. $12$

Q. If $19$th term of a non-zero A.P. is zero, then its ($49$th term) : ($29$th term) is :

1. $4:1$
2. $1:3$
3. $2:1$
4. $3:1$

Q. A man starts repaying a loan as first installment of Rs. 100. If he increases the installment by Rs 5 every month, what amount he will pay in the 30 th installment?

Q. A man deposited Rs 10000 in a bank at the rate of 5% simple interest annually. Find the amount in 15 th year since he deposited the amount and also calculate the total amount after 20 years.

Q. If $x_1,x_2,\cdots ,x_n$ and $\frac{1}{h_1},\frac{1}{h_2},\cdots ,\frac{1}{h_n}$ are two $A.P.$s such that $x_3=h_2=8$ and $x_8=h_7=20,$ then $x_5\cdot h_{10}$ equals

1. $2560$
2. $2650$
3. $3200$
4. $1600$

Q.

The sum and sum of squares corresponding to length $x$ (in cm) and weight $y$ (in gm) of 50 plant products are given below :

${\sum }_{i=1}^{50}{x}_i=212,{\sum }_{i=1}^{50}{x}_i^2=902.8,{\sum }_{i=1}^{50}{y}_i=261,{\sum }_{i=1}^{50}{y}_i^2=1457.6$

Which is more varying, the length or the weight ?

Q.

The sum of 9 terms of G.P. 3, 6, 12, ... is:

1. 

2. 3069

3. 

4. 1533

Q. If $a_n$ is the $n^{\text{th}}$ of an A.P. such that $a_2+a_7-a_4=11$ and $a_3+a_8=24,$ then

1. commom difference is $2$
2. first term is $2$
3. $a_7=14$
4. $a_{10}=21$

Q. 6.3×8+6×11+9×14+…

Q.

Three terms in A.P. are such that their sum is 45.What is the middle term?

1. 15

2. 30

3. 10

4. 25

Q. The largest number common to both the sequences $1,11,21,31,\cdots \text{upto}100\text{terms}$ and $31,36,41,46,\cdots \text{upto}100\text{terms}$ is

1. $531$
2. $501$
3. $511$
4. $521$

Q. If in an A.P. pth term is q and the (p+q)th term is 0. Then, its qth term is

1. -p
2. p
3. p-q
4. p+q

Q.

In a cricket tournament 16 school teams participated. A sum of Rs.16000 is to be awarded among themselves as prize money. If the team in the last place is awarded RS 550 in prize money and the award increases by the same amount for successive finishing places, how much amount will the team in the first place receive?

Q. Find the sum to n terms of the A.P., whose k th term is 5 k + 1.

Q. If the sum of a certain number of terms of the A.P. 25, 22, 19, … is 116. Find the last term

Q. If n^th terms of two A.P.'s are 3n + 8 and 7n + 15, then the ratio of their 12^th terms will be
[MP PET 1986]

1. 4/9

2. 7/16

3. 3/7
4. 8/15

Q.

If the sides of a right angle triangle from an AP, the sine of the acute angles are

1. 

2. 

3. 

4. 

Q. If $100$ times the ${100}^{th}$ term of an A.P. is equal to the $50$ times the ${50}^{th}$ term, then the value of ${150}^{th}$ term of this A.P. is

1. $0$
2. $150$
3. $50$
4. dependent on the value of the first term.

Q. If the A.M. of two positive numbers a and b (a > b) is twice their geometric mean. Prove that: $a:b=(2+\sqrt{3}):(2-\sqrt{3}).$

Q. In a G.P. if the (m + n)^th term is p and (m − n)^th term is q, then its m^th term is
(a) 0
(b) pq
(c) $\sqrt{pq}$
(d) $\frac{1}{2}(p+q)$

Q.

Find the coefficient of $(a^5+b^4+c^7)$ in the expansion of $(bc+ca+ab{)}^8$

___

Q.

Write the first five terms of the sequences whose $n^{th}$ term is :

$a_n=(-1{)}^{n-1}.5^{n+1}$

Q.

Solve for x if (x-1) (x-2) (x-5) > 0

1. [1, 2]U[5, ]

2. (1, 2)U(5, )

3. (, 1) U (2, 5)

4. (2, 5)

Q.

A man starts repaying a loan as first instalment of Rs. 100. If he increases the instalment by Rs. 5 every month, what amount he will pay in the ${30}^{th}$ instalment ?

Q. If '$S$' is sum of all real values of '$x$' satisfying the equation $lo{g}_{1/2}\left(lo{g}_2\right(x+\sqrt{5})+lo{g}_2(x-\sqrt{5})+lo{g}_{1/2}(x-2\left)\right)-1$, then '$S$' is equal to

1. a rational number
2. a whole number
3. neither prime nor composite
4. a prime number

Q. If sum of $n$ of a series is given by $S_n=3n^2+3n$, then $n^{th}$ term of the series is

1. $3n$
2. $3n+10$
3. $6n$
4. $6n+10$

Q. If $n^{th}$ of a sequence is given by $T_n=2n+1$, then the sum of $4$ terms is

1. $16$
2. $24$
3. $28$
4. $32$

Q. If the $n\text{th}$ term of a sequence is given by $t_n=8n+3$, then the sum of first $20$ terms is

1. $1720$
2. $1330$
3. $1800$
4. $1740$

Q. 23.Find the sum of the first n terms of the series: 3+ 7 +13 +21 +31 +

Q. The ${10}^{\text{th}}$ term common between the series $3+7+11+15+...$ and $1+6+11+16+...$ is