nth Term of A.P

Q. The number of terms common to the two arithmetic progressions
$3,7,11,\dots ,407$ and $2,9,16,\dots ,709$ is

Q.

The sequence $\frac{5}{\sqrt{7}},\frac{6}{\sqrt{7}},\sqrt{7}....$ is

1. HP

2. GP

3. AP

4. None of these

Q.

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

Q.

The solution of the equation $(\mathrm{x}+1)+(\mathrm{x}+4)+(\mathrm{x}+7)+....(\mathrm{x}+28)=155$ is

1. $1$

2. $2$

3. $3$

4. $4$

Q. If the product of three consecutive numbers in A.P. is $224$ and the largest number is $7$ times the smallest, then which of the following is (are) CORRECT?

1. The smallest number is $4$.
2. The sum of all the three numbers is $10$.
3. The smallest number is $2$.
4. The sum of all the three numbers is $24$.

Q.

Let $a_{1,}{a}_{2,...,}{a}_{49}$be in AP such that $\sum _{k=0}^{12}{a}_{4k+1}=416$ and $a_9+a_{43}=66$. If ${a_1}^2+{a_2}^2+...{+a_{17}}^2=140\text{m}$, then $\text{m}$ is equal to:

1. $34$

2. $33$

3. $66$

4. $68$

Q.

How many terms of the A.P. $9,17,25,...$ must be taken so that their sum is $636$?

Q.

Let $a_n$ be the $n^{th}$ term of an AP. If $\sum _{r=1}^{100}{a}_{2r}=\alpha$ and $\sum _{r=1}^{100}{a}_{2r-1}=\beta$, then the common difference of an AP is

1. $\frac{(\alpha -\beta )}{200}$

2. $\frac{(\alpha -\beta )}{100}$

3. $(\alpha -\beta )$

4. $\beta -\alpha$

Q.

The sixth term of an A.P is equal to $2$, the value of the common difference of the A.P. which makes the product $a_1{a}_4{a}_5$ least is given by

1. $x=\frac{8}{5}$

2. $x=\frac{5}{4}$

3. $x=\frac{2}{3}$

4. none of these

Q. Let $a_1,a_2,a_3,\dots$ be an A.P. such that $a_3+a_5+a_8=11$ and $a_4+a_2=-2$. Then the value of $a_1+a_6+a_7$ is

1. $-8$
2. $5$
3. $7$
4. $9$

Q.

The value of the common difference of an arithmetic progression, which makes $T_1{T}_2{T}_7$ the least. Given that, $T_7=9$ is

1. $\frac{33}{2}$

2. $\frac{5}{4}$

3. $\frac{33}{20}$

4. None of these.

Q.

Six numbers are in an AP such that their sum is $3$. The first term is $4$ times the third term. Then, the fifth term is

1. $-15$

2. $-3$

3. $9$

4. $-4$

Q. Which of the following can be terms (not necessarily consecutive) of any A.P. ?

1. $1,6,19$
2. $\sqrt{2},\sqrt{50},\sqrt{98}$
3. $\log 2,\log 16,\log 128$
4. $\sqrt{2},\sqrt{3},\sqrt{7}$

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

Q.

If the Arithmetic Mean (AM) of two numbers is $A$ and Geomatics Mean (GM) is $G$, then the numbers will be

1. $A\pm (A^2-G^2)$

2. $\sqrt{A}\pm \sqrt{(A^2-G^2)}$

3. $A\pm \sqrt{(A+G)(A-G)}$

4. $\frac{(A\pm \sqrt{(A+G)(A-G)})}{2}$

Q.

How many positive integers between $1000$ and $9999$ inclusive are divisible by nine?

Q. The number of terms in the sequence $3,7,11,\dots ,407$ is

1. $102$
2. $103$
3. $104$
4. $101$

Q. If a sequence is given by $9,12,15,18,\cdots$, then the value of ${16}^{th}$ term is

1. $50$
2. $52$
3. $54$
4. $56$

Q.

Find the common difference of the A.P. and write the next two terms:$75,67,59,51,...$

Q.

Write the first three terms of the $\mathrm{APs}$ when $a$ and $d$ are as given below:$\left(3\right)a=\sqrt{2},d=\frac{1}{\sqrt{2}}$

Q. The ${17}^{th}$ term from the end of the A.P. $-36,-31,-26,...,79$ is

1. $9$
2. $4$
3. $-6$
4. $-1$

Q.

Which term of the A.P. $3,8,13,18,...$ is $78$?

Q. Let $p,q$ be the roots of the equation $x^2-2x+A=0$ and let $r,s$ be the roots of the equation $x^2-18x+B=0.$ If $p,q,r,s$ with $p<q<r<s$ are in A.P., then

1. $A=-3$
2. $B=-77$
3. $B=77$
4. $A=3$

Q. If $f:A\to B,g:B\to A$ be two functions such that $gof=I_A$, then which among following is/are correct?

1. $f$ is many-one function.
2. $g$ is an into function.
3. $g$ is a surjective function.
4. $f$ is an injective function.

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. Let $T_r$ be the $r^{th}$ term of an A.P. for $r=1,2,3,\dots$ If for some positive integers $m,n$, $T_m=\frac{1}{n}$ and $T_n=\frac{1}{m}$, then $T_{mn}$ equals

1. $\frac{1}{mn}$
2. $\frac{1}{m}+\frac{1}{n}$
3. $1$
4. $0$

Q.

In an AP, the $p^{th}$ term is$q$and ${(p+q)}^{th}$ term is $0$. Show that its $q^{th}$ term is$p$.

Q. The smallest positive term of the sequence $25,22\frac{3}{4},20\frac{1}{2},18\frac{1}{4},\cdots$ is

1. $7$
2. $\frac{19}{4}$
3. $\frac{5}{2}$
4. $\frac{1}{4}$

Q. If sum of $n$ terms of a series is given by $S_n=3n^2+3n$, then $6^{th}$ term of the series is

Q. The first negetive term in the sequence of $56,55\frac{1}{5},54\frac{2}{5},\cdots$

1. ${71}^{th}$
2. ${70}^{th}$
3. ${72}^{th}$
4. ${73}^{th}$