Sum of N Terms of an AP

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

1. 6
2. 8
3. 9
4. 12

Q.

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

1. $2^{-\mathrm{n}}$

2. $2^{-\mathrm{n}}(\mathrm{n}–1)$

3. $2^{\mathrm{n}}(\mathrm{n}–1)+1$

4. $2^{-\mathrm{n}}+\mathrm{n}–1$

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 m²: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 $\frac{2}{7}$?

1. $16:72$

2. $16:56$

3. $14:56$

4. $15:56$

Q.

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

Q. Which number would replace the question mark in series,
7, 12 , 19 , ? , 39

1. 24
2. 31
3. 28
4. 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

1. $310$

2. $300$

3. $320$

4. 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 _____.

1. $a+b:c$
2. $a+c:d$
3. $a+d:c$
4. $a+c:b+d$

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 $₹3250$ by paying $₹20$ in the first month and then increases the payment by $₹15$ every month. How long will it take him to clear the loan?

Q. $\text{What is the sum of first 11 odd numbers?}$

1. 107
2. 93
3. 121
4. 115

Q. $log2+16log\frac{16}{15}+12log\frac{25}{24}+7log\frac{81}{80}$

Q.

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

1. ${\log }_{e}2–\frac{1}{2}$

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

3. ${\log }_{e}2+\frac{1}{2}$

4. ${\log }_{e}2+1$

Q.

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

1. $5\frac{1}{5}$

2. $3\frac{1}{5}$

3. $\frac{1}{10}$

4. $10$

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

1. $2a$

2. $2m$

3. $a+4$

4. $m+4$

Q.

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

1. $8$

2. $10$

3. $15$

4. $20$

Q.

Question 23
If $a_n=3-4n$, then show that $a_1,a_2,a_3,\cdots$ form an AP. Also, find $S_{20}$.

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?