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Sequence and Series - Set 1

Home
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NUST Entrance Test
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Mathematics
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Sequence and Series

Set 1

MM

Mashaal Masha

Sep 29, 2022

On this page

$Which of the following series converges?$
$\sum_{n=0}^\infty \frac{1}{2^{n-1}}=$
$Calculate $S_{8}$ when $a_{1}=8$ and $r= -\frac{1}{2}$$
$The 11th term of the series $2,\frac{5}{2},3\space ...$ will be$
$\sum_{n=0}^\infty \frac{1}{2^{n}}=$
$What is the G.M of $32$ and $64$$
$Sum the series $1+3+5+\space...$ up to $n$ terms$
$What are the three AMs between $-18$ and $4$?$
$What is the sum of the first 50 natural numbers?$
$What is the nth term of the sequence $1,3,5,7 \space ...$$

Choose the correct options for the following questions.

Which of the following series converges?

Difficulty: Easy

A:

S=-1-1-1- \space...

B:

S=1+\frac{1}{2}+\frac{1}{4} + \space...

C:

S=1+1+1+ \space...

D:

S=2+4+8+ \space...

View Solution Steps

\sum_{n=0}^\infty \frac{1}{2^{n-1}}=

Difficulty: Easy

A:

Which of the following series converges?

B:

$-2$

C:

4

D:

16

View Solution Steps

Calculate $S_{8}$ when $a_{1}=8$ and $r= -\frac{1}{2}$

Difficulty: Easy

A:

-\frac{25}{2}

B:

\frac{85}{16}

C:

\frac{55}{8}

D:

-\frac{95}{32}

View Solution Steps

The 11th term of the series $2,\frac{5}{2},3\space ...$ will be

Difficulty: Easy

A:

\frac{11}{2}

B:

\frac{14}{2}

C:

\frac{11}{2}

D:

\frac{22}{2}

View Solution Steps

\sum_{n=0}^\infty \frac{1}{2^{n}}=

Difficulty: Easy

A:

\frac{1}{2}

B:

1

C:

2

D:

4

View Solution Steps

What is the G.M of $32$ and $64$

Difficulty: Easy

A:

$45.25$

B:

$48$

C:

$-48$

D:

$-45.25$

View Solution Steps

Sum the series $1+3+5+\space...$ up to $n$ terms

Difficulty: Easy

A:

n^{2}

B:

ln $e^{2}$

C:

2^{n}

D:

n^{e}

View Solution Steps

What are the three AMs between $-18$ and $4$?

Difficulty: Easy

A:

$1,2,3$

B:

$12.5,7,1.5$

C:

$-12.5,-7,-1.5$

D:

AM can not be found between a negative and a positive number

View Solution Steps

What is the sum of the first 50 natural numbers?

Difficulty: Easy

A:

500

B:

1200

C:

1275

D:

8900

View Solution Steps

What is the nth term of the sequence $1,3,5,7 \space ...$

Difficulty: Easy

A:

$2n - 1$

B:

$2n + 3$

C:

$2n$

D:

It is impossible to find the nth term for such a sequence

View Solution Steps