# nth Term of A.P

## Trending Questions

**Q.**The number of terms common to the two arithmetic progressions

3, 7, 11, …, 407 and 2, 9, 16, …, 709 is

**Q.**

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

HP

GP

AP

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

$1$

$2$

$3$

$4$

**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?

- The smallest number is 4.
- The sum of all the three numbers is 10.
- The smallest number is 2.
- 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:

$34$

$33$

$66$

$68$

**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

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

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

$(\alpha -\beta )$

$\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

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

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

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

none of these

**Q.**Let a1, a2, a3, … be an A.P. such that a3+a5+a8=11 and a4+a2=−2. Then the value of a1+a6+a7 is

- −8
- 5
- 7
- 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

$\frac{33}{2}$

$\frac{5}{4}$

$\frac{33}{20}$

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

$-15$

$-3$

$9$

$-4$

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

- 1, 6, 19
- √2, √50, √98
- log2, log16, log128
- √2, √3, √7

**Q.**The largest number common to both the sequences 1, 11, 21, 31, ⋯ upto 100 terms and 31, 36, 41, 46, ⋯ upto 100 terms is

- 511
- 521
- 531
- 501

**Q.**

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

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

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

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

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

**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, …, 407 is

- 102
- 103
- 104
- 101

**Q.**If a sequence is given by 9, 12, 15, 18, ⋯, then the value of 16th term is

- 50
- 52
- 54
- 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 17th term from the end of the A.P. −36, −31, −26, ..., 79 is

- 9
- 4
- −6
- −1

**Q.**

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

**Q.**Let p, q be the roots of the equation x2−2x+A=0 and let r, s be the roots of the equation x2−18x+B=0. If p, q, r, s with p<q<r<s are in A.P., then

- A=−3
- B=−77
- B=77
- A=3

**Q.**If f:A→B, g:B→A be two functions such that gof=IA, then which among following is/are correct?

- f is many-one function.
- g is an into function.
- g is a surjective function.
- f is an injective function.

**Q.**If the nth term of a sequence is given by tn=8n+3, then the sum of first 20 terms is

- 1720
- 1330
- 1800
- 1740

**Q.**Let Tr be the rth term of an A.P. for r=1, 2, 3, … If for some positive integers m, n, Tm=1n and Tn=1m, then Tmn equals

- 1mn
- 1m+1n
- 1
- 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, 2234, 2012, 1814, ⋯ is

- 7
- 194
- 52
- 14

**Q.**If sum of n terms of a series is given by Sn=3n2+3n, then 6th term of the series is

**Q.**The first negetive term in the sequence of 56, 5515, 5425, ⋯

- 71th
- 70th
- 72th
- 73th