Sum of n Terms

Q.

${14}^{\frac{1}{7}}\times {14}^{\frac{1}{7}}$ can be represented as

1. (14)^{1/7 + 1/7}

2. (14 x 14)^1/7

3. (14²)^1/7

4. All of the above

Q.

The first term of an A.P of consecutive integers is $p^2+1$. The sum of$(2p+1)$ terms of this series can be expressed as

1. ${(p+1)}^2$

2. ${(p+1)}^3$

3. $(2p+1){(p+1)}^2$

4. $p^3+{(p+1)}^3$

Q.

A person sends an SMS to four friends with the instruction that it has to be sent to four of their friends. Considering the fact that the chain is not broken and that it costs 50 paise to send one message, find the amount spent when the eighth set of messages is sent.

1. ₹ 73, 690

2. ₹ 44, 690

3. ₹ 43, 690

4. ₹ 43, 698

Q. if the ratio of the sums of first n terms of two A.P. is 7n+1÷4n+27 find ratio of their ninth term.

Q.

4 + 44 + 444 + .................upto $n$ terms = __

1. $\frac{40}{81}\left({10}^n\right)+\frac{4n}{9}$

2. $\frac{40}{81}({10}^n+1)+\frac{4n}{9}$

3. $\frac{40}{81}\left({10}^n\right)-\frac{4n}{9}$

4. $\frac{40}{81}({10}^n-1)-\frac{4n}{9}$

Q.

Question 91

A picture hall has seats for 820 persons. At a recent film show, one usher guessed it was $\frac{3}{4}$ full, another that it was $\frac{2}{3}$ full. The ticket office reported 648 sales. Which usher (first or second ) made the better guess?

Q.

A father left a will of Rs $16,400$ for his two sons aged $17$ and $18$ years. They must get equal amounts when they are $20$ years at $5$ compound interest. Find the present share of the elder son.

___

Q. If (4x²–3y²):(2x²+5y²)=12:19, find x:y

Q. Question 3
The product of three consecutive positive integers is divisible by 6: Is this statement true or false? Justify your answer.

Q.

A man completes 3/8 of a job in 12 days. At this rate, how many more days will it take him to finish the job?

1. 10

2. 25

3. 15

4. 20

Q. The sum of n terms of two A.P.s are in the ratio 5n + 9 : 9n + 6. Then, the ratio of their 18th term is

(a) $\frac{179}{321}$

(b) $\frac{178}{321}$

(c) $\frac{175}{321}$

(d) $\frac{176}{321}$

Q. 1, 3, 6, 10, ___, 21. Missing term in the sequence is

1. 12
2. 15
3. 18

Q. If 18^th and 11^th term of an A.P. are in the ratio 3 : 2, then its 21^st and 5^th terms are in the ratio

(a) 3 : 2

(b) 3 : 1

(c) 1 : 3

(d) 2 : 3

Q.

How many terms of the geometric progression 1 + 4 + 16 + 64 + ........ must be added to get sum equal to 5461 ?

Q.

If the sum of $1+2+2^2+................+2^{n-1}$ is 255. find the value of n.

Q.

If $b^2,a^2,c^2$are in A.P., then $a+b,b+c,c+a,$ will be in

1. A.P

2. G.P

3. H.P

4. None of these

Q.

A contractor has two teams of workers: team A and team B. Team A can complete a
job in 12 days and team B can do the same job in 36 days. Team A starts working on
the job and team B joins team A after four days. The team A withdraws after two more
days. For how many more days should team B work to complete the job?

Q. How to know the splitting numbers in splitting the middle term method ?? ( especially big no's )

Q.

$\frac{2}{1}\times \frac{1}{3}+\frac{3}{2}\times \frac{1}{9}+\frac{4}{3}\times \frac{1}{27}+\frac{5}{4}\times \frac{1}{81}+...........$is equal to

1. $\frac{1}{2}+{\log }_e\left(\frac{3}{2}\right)$

2. ${\log }_e\left(3\right)-{\log }_e\left(2\right)$

3. ${\log }_e\left(6\right)$

4. ${\log }_e\left(2\right)-{\log }_e\left(3\right)$

Q.

Find the sum of all natural numbers lying between 100 and 500 which are divisible by 8

Q. If Sn, the sum of first n terms of an AP, is given by
$S_n$ = $5n^2$ - 2n, find the common difference of the AP.

Q.

There were $500$ soldiers in a fort. They had enough food for $30days$ but $125$ soldiers were transferred to another fort. For how many days did the food last now?

Q.

In a G.P., the ratio between the sum of first three terms and that of the first six terms is 125 : 152.

Find its common ratio.

Q. Question 19
Subba Rao started work in 1995 at an annual salary of ₹ 5000 and received an increment of ₹ 200 each year. In which year did his income reach ₹ 7000?

Q. 24 The ratio of the sum of n terms of two A.Ps is (3n-13):(5n+21). The ratio of 24th terms of the two progressions is a. 1:2 b. 2:3 c. 3:5 d. 7:11

Q.

Question 4 (iv)
Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.
(iv) -10, - 6, - 2, 2 …

Q. given l = 28, S = 144, and there are total 9 terms. Find a.

Q. 23. If the sum of first n terms of an AP is 4n-nxn , what is the first term ( that is s1 ) ? What is the sum of first two terms? What is the second term? Similarly find the 3rd , the 10 the and the nth terms

Q. The sum of n terms of two arithmetic progressions are in the ratio ( 3n+8) : ( 7n +15). Find the ratio of their 12th terms.

Q.

What is $r$ in geometric progression?