# Sum of N Terms of an AP

## Trending Questions

**Q.**Three numbers are in A.P. If the sum of these numbers are 27 and the product is 648, find the numbers.

- 6
- 8
- 9
- 12

**Q.**

Sum of $n$ terms of the series$\frac{1}{2}+\frac{3}{4}+\frac{7}{8}+\frac{15}{16}+......$ is

${2}^{-\mathrm{n}}$

${2}^{-\mathrm{n}}(\mathrm{n}\u20131)$

${2}^{\mathrm{n}}(\mathrm{n}\u20131)+1$

${2}^{-\mathrm{n}}+\mathrm{n}\u20131$

**Q.**Seven years ago Varun's age was five times the square of Swati's age. Three years hence Swati's age will be two fifth of Varun's age. Find their present ages.

[4 MARKS]

**Q.**If the ratio of the sum of the first m and n terms of an AP is m

^{2}:n

^{2 }. Show that the ratio of it's m

^{th}and n

^{th }terms is (2m-1):(2n-1)

**Q.**

Find four numbers in A.P. whose sum is 20 and the sum of whose squares is 120.

**Q.**

Question 87

Solve the following:

Find a number whose fifth part increased by 30 is equal to its fourth part decreased by 30.

**Q.**

What is the ratio whose terms differ by 40 and the measure of which is 27?

16:72

16:56

14:56

15:56

**Q.**

Solve$2\mathrm{x}-1=14-\mathrm{x}$.

**Q.**Which number would replace the question mark in series,

7, 12 , 19 , ? , 39

- 24
- 31
- 28
- 26

**Q.**

Hectors school is holding a fitness challenge.

Student are encouraged to exercise at least $2\frac{1}{2}$ hours per week.

Hector exercises about the same number of hours each week.

During a $4$-week period, he exercises for $11\frac{1}{2}$ hours.

Hector wants to compare his exercise rate with the fitness challenge rate.

How many hours per week does Hector exercise?

**Q.**

The maximum sum of the series $20+19\frac{1}{3}+18\frac{2}{3}+...$ is

$310$

$300$

$320$

none of these

**Q.**

Find the sum of the first five multiples of $3$.

**Q.**

What is the sum of first $20$ natural numbers?

**Q.**Find the sum of first 8 multiples of 3.

**Q.**Question 3 (i)

In the following APs, find the missing term in the boxes.

**Q.**If a:b=c:d, then according to theorem of equal ratios a:b is also equal to _____.

- a+b:c
- a+c:d
- a+d:c
- a+c:b+d

**Q.**

How many even numbers are there between $1$ to $100$?

**Q.**

Question 119 (vii)

Write two integers which are greater than -4 but their difference is smaller than -4.

**Q.**

A man repays a loan of $\u20b93250$ by paying $\u20b920$ in the first month and then increases the payment by $\u20b915$ every month. How long will it take him to clear the loan?

**Q.**What is the sum of first 11 odd numbers?

- 107
- 93
- 121
- 115

**Q.**log2+16log1615+12log2524+7log8180

**Q.**

The sum of series $\frac{1}{1.2.3}+\frac{1}{3.4.5}+\frac{1}{5.6.7}+\dots .$is

${\mathrm{log}}_{e}2\u2013\frac{1}{2}$

${\mathrm{log}}_{e}2$

${\mathrm{log}}_{e}2+\frac{1}{2}$

${\mathrm{log}}_{e}2+1$

**Q.**

The fifth term of the HP $2,2\frac{1}{2},3\frac{1}{3}$ will be

$5\frac{1}{5}$

$3\frac{1}{5}$

$\frac{1}{10}$

$10$

**Q.**Question 1 (ii)

Find the sum of the following APs

(ii) − 37, − 33, − 29 , …, to 12 terms

**Q.**

The arithmetic mean of $7$ consecutive integers starting with $a$ is $m$. Then, the arithmetic mean of $11$ consecutive integers starting with $a+2$ is

$2a$

$2m$

$a+4$

$m+4$

**Q.**

Sum of the squares of first $n$ natural numbers exceeds their sum by $330$, then $n$ equals

$8$

$10$

$15$

$20$

**Q.**

**Question 23**

If an=3−4n, then show that a1, a2, a3, ⋯ form an AP. Also, find S20.

**Q.**

A recursive rule for an arithmetic sequence is ${a}_{1}=4$ ; ${a}_{n}={a}_{n-1}+3$ .

What is an explicit rule for this sequence?

**Q.**

Question 97

Solve the following:

Find the product of the cube of (-2) and the square of (+4).

**Q.**Question 14

How many multiples of 4 lie between 10 and 250?