Sum of n Terms of a GP

Q.

Choose the correct option.$46:64::82:?$

1. $100$

2. $104$

3. $48$

4. $42$

Q.

The taxi fare after each km when the fare is Rs $15$ for the first km and Rs $8$ for each additional km. Write the arithmetic progression thus formed.

Q.

Find the $6^{\mathrm{th}}$ term from the end of the GP $8,4,2$$.....\frac{1}{1024}$

Q.

The sum of first 20 terms of the sequence 0.3, 0.33, 0.333, ....., is

1. $\frac{1}{27}[189+(10{)}^{-20}]$

2. $\frac{1}{27}[179+(10{)}^{-20}]$

3. $\frac{1}{27}[149+(10{)}^{-20}]$

4. $\frac{1}{27}[255+(10{)}^{-20}]$

Q. $\mathrm{Find}\mathrm{the}\mathrm{least}\mathrm{positive}\mathrm{integer}\mathrm{such}\mathrm{that}1+7+7^2+7^3+....+7^n>3500$

1. 6
2. 8
3. 7
4. 6

Q.

Find the sum of first ${12}^{th}$ term of the GP, whose $8^{th}$ term is $192$ and the common ratio is $2$.

Q.

How many terms of the series 1, 4, 16, ..... must be taken to have their sum equal to 341 ?

1. 3

2. 6

3. 4

4. 5

Q.

How many terms of the GP $\frac{8}{9},\frac{8}{18},\frac{8}{36}$..... should be added to get the sum $\frac{31}{18}$?

1. 3

2. 5

3. 6

4. 4

Q. The sum of first 20 terms of the sequence 0.5, 0.55, 0.555, ...., is ___.

1. $\frac{5}{81}(179-{10}^{-20})$
2. $\frac{5}{9}(99-{10}^{-20})$
3. $\frac{5}{81}(179+{10}^{-20})$
4. $\frac{5}{9}(99+{10}^{-20})$

Q. The sum of the first 20 terms of the sequence 0.7, 0.77, 0.777, ....., is ___.

1. $\frac{7}{81}(179-{10}^{-20})$
2. $\frac{7}{9}(99-{10}^{-20})$
3. $\frac{7}{81}(179+{10}^{-20})$
4. $\frac{7}{9}(99+{10}^{-20})$

Q.

The sum of the first $n$ terms of the series
$\frac{1}{2}+\frac{3}{4}+\frac{7}{8}+\frac{15}{16}+\cdots$ is equal to ___.

1. $n+2^{-n}-1$

2. $2^n+1.$

3. $2^n-n-1$

4. $1-2^{-n}$

Q.

How many terms of the GP $\frac{8}{9},\frac{8}{18},\frac{8}{36}$..... should be added to get the sum $\frac{31}{18}$?

Q.

The sum of the first $n$ terms of the series
$\frac{1}{2}+\frac{3}{4}+\frac{7}{8}+\frac{15}{16}+\cdots$ is equal to ___.

1. $n+2^{-n}-1$

2. $2^n-n-1$

3. $2^n+1.$

4. $1-2^{-n}$

Q.

$1+3^1+3^2+3^3..........+3^{2999}$ =

1. $\frac{5^{2999}-1}{2}$

2. $\frac{3^{3000}-1}{2}$

3. $\frac{3^{2999}-1}{2}$

4. $\frac{4^{1999}-1}{2}$

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, 698

4. ₹ 43, 690

Q.

8 + 88 + 888 + .............n terms = ____

1. $\frac{80}{81}({10}^n-1)-\frac{8n}{9}$

2. $\frac{10}{81}({10}^n-1)$

3. $\frac{80}{81}({10}^n-1)+\frac{8n}{9}$

4. $\frac{80}{81}({10}^n-1)-\frac{n}{9}$