Arithmetic Progressions Test

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Arithmetic Progressions Test - 19

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Question 1
1 / -0

Is $$-150$$ a term of the $$A.P$$ : $$11, 8, 5, 2$$ ?

A
No

B
Yes

C
Data Insufficient

D
Can't say

Solution

Clearly the given sequence is an AP with first term $$a=11$$ and the common difference $$d=8-11=-3$$.

Let $$-150$$ be the $$n^{th}$$ term of given AP. Then,
$$a_n=-150\Rightarrow t_n= a+(n-1)d=-150$$
$$\Rightarrow 11+(n-1)\times-3=-150$$
$$\Rightarrow (n-1)\times-3=-161$$
$$\Rightarrow n-1=\dfrac{-161}{-3}$$
$$\Rightarrow n=\dfrac{161}{3}+1=\dfrac{164}3$$
Clearly $$n$$ is not an natural number, Hence, $$-150$$ is not a term of given AP.
Question 2
1 / -0

Find the nth term and 9th term of the sequence 3, 7, 11, 15.........

A
$$4n-1$$ and $$T_9=35$$

B
$$4n+1$$ and $$T_9=37$$

C
$$2n-1$$ and $$T_9=35$$

D
$$4n-1$$ and $$T_9=39$$

Solution

We know,
$$n^{th}$$ term $$a_{n}= a+(n-1)d $$

$$a =$$ First term
$$d =$$ Common difference
$$n =$$ number of terms
$$a_n = n^{th}$$ term

Here,
$$a=3\ and\ d=7-3\ or\ 11-7=4$$

$$a_n=a+(n-1)d=3+(n-1)4$$
$$a_n=4n-1$$

For $$9$$th term put $$n=9$$
$$T_9=a_9=4\times9-1=35$$
Question 3
1 / -0

Write the first term $$a$$ and the common difference $$d$$ of the AP : $$-5, -1, 3, 7......$$

A
$$a = -5, d = 4$$

B
$$a =-5, d = -6$$

C
$$a = -5, d = -4$$

D
$$a = 5, d = -4$$

Solution

Given series is $$-5, -1, 3,7,......$$
Clearly first term is $$a=-5$$
And common difference $$d=-1-(-5)=4$$
Question 4
1 / -0

Find out whether the sequence $$1^2, 3^2, 5^2, 7^2$$,... is an AP. If it is, find out the common difference.

A
No

B
Yes, $$d=8$$

C
Yes, $$d=-8$$

D
Yes, $$d=9$$

Solution

Given series is $$1^2, 3^2, 5^2, 7^2,......$$
We have, $$3^2-1^2=9-1=8$$
$$5^2-3^2=25-9=16$$
$$7^2-5^2=49-25=24$$
This shows that the difference of a term and the preceding term is not always same.
Hence, the given sequence is not an AP.
Question 5
1 / -0

Check if the series is an AP. Find the common difference $$d$$ and write three more terms of the the following series.
$$2, 4, 8, 16,....$$

A
Common difference: $$2$$ and Other three terms are: $$32, 64, 128$$

B
Common difference: $$4$$ and Other three terms are: $$24, 32, 40$$

C
Common difference: $$8$$ and Other three terms are: $$20, 24, 28$$

D
None of these

Solution

Given series is $$2,4,8,16,.....$$

In an AP series, the difference between the consecutive terms remain same:
$$a_2-a_1=4-2=2$$

$$a_3-a_2=8-4=4$$

$$a_3-a_2\neq a_2-a_1$$

This shows that the difference of a term and the preceding terms is not always same. Hence, the given sequence is not an AP.
Question 6
1 / -0

Find first term 'a' and common difference 'd' for the following AP.

$$\sqrt{2}$$, $$\sqrt{8}$$, $$\sqrt{18}$$, $$\sqrt{32}$$,.....

A
$$a =$$ $$\sqrt{2}$$$$, d=$$ $$\sqrt{4}$$

B
$$a =$$ $$\sqrt{2}$$$$, d=$$ $$\sqrt{2}$$

C
Its not an AP

D
None of these

Solution

The sequence $$\sqrt2,\sqrt8,\sqrt{18},\sqrt{32},...$$ can be written as $$\sqrt2,2\sqrt2,3\sqrt2,4\sqrt{2},...$$
Clearly, it is an AP with first term $$a=\sqrt2$$ and common difference $$d=\sqrt2$$.
Question 7
1 / -0

Check if the series is an A.P. Find the common difference $$d$$ and write three more terms of the the following series.
$$2,\displaystyle\frac{5}{2}$$, $$3,\displaystyle\frac{7}{2}, ...$$

A
$$a=2$$; $$d=\dfrac{1}{2}$$; other terms $$4,$$ $$\dfrac{9}{2},5$$

B
$$a=3$$; $$d=\dfrac{1}{2}$$; other terms $$6, 8, 10$$

C
$$a=2$$; $$d=\dfrac{3}{2}$$; other terms $$7, 8, 15$$

D
$$a=3$$; $$d=\dfrac{3}{2}$$; other terms $$4, 5, 15$$

Solution

It is an A.P. because $$a = 2$$, $$d = \dfrac12$$
$$\because [(t_2 - t_1) = (t_3 - t_2) = (t_4 - t_3) = \dfrac12]$$
$$t_5 = \dfrac{7}{2} + \dfrac{1}{2} = 4$$
$$t_6 = 4 + \dfrac{1}{2} = \dfrac{9}{2}$$
$$t_7 = \dfrac{9}{2} + \dfrac{1}{2}= 5$$
Question 8
1 / -0

For the following AP, write the first term and the common difference
$$3, 1, -1, -3$$

A
First term: $$-3$$ and Common difference: $$2$$

B
First term: $$-1$$ and Common difference: $$-3$$

C
First term: $$1$$ and Common difference: $$3$$

D
First term: $$3$$ and Common difference: $$-2$$

Solution

Given series is $$3,1,-1,-3,......$$
First term $$a=3$$
And common difference $$d=a_2-a_1$$
$$=1-3$$
$$=-2$$.
Question 9
1 / -0

Write first four terms of the AP, when the first term $$a$$ and the common difference $$d$$ are given as follows:
$$a = 10, d =10$$

A
The first four terms of the AP are $$20, 40, 60, 80.$$

B
The first four terms of the AP are $$10, 20, 30, 40.$$

C
The first four terms of the AP are $$15, 30, 45, 60.$$

D
Data insufficient

Solution

Here $$a=10$$ and $$d=10$$.

Now, $$n^{th}$$ term $$=a_n=a+(n-1)d$$

$$\therefore t_1=a=10$$

$$t_2=a+d=10+10=20$$

$$t_3=a+2d=10+2\times10=30$$

$$t_4=a+3d=10+3\times10=40$$

Thus, the first four terms of given AP are $$10,20,30,40$$.
Question 10
1 / -0

For the following AP, write the first term and the common difference
$$-5, -1, 3, 7$$

A
First term: $$7$$ and Common difference: $$7$$

B
First term: $$3$$ and Common difference: $$-1$$

C
First term: $$-5$$ and Common difference: $$4$$

D
First term: $$3$$ and Common difference: $$-2$$

Solution

Given series is $$-5,-1,3,7,....$$
First term $$a=-5$$
And common difference $$d=a_2-a_1$$
$$=-1-(-5)$$
$$=-1+5$$
$$=4$$

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Re-Attempt Weekly Quiz Competition

Arithmetic Progressions Test - 19

Result

Arithmetic Progressions Test - 19

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SHARING IS CARING

Question 1

No

Yes

Data Insufficient

Can't say

Solution

Question 2

$$4n-1$$ and $$T_9=35$$

$$4n+1$$ and $$T_9=37$$

$$2n-1$$ and $$T_9=35$$

$$4n-1$$ and $$T_9=39$$

Solution

Question 3

$$a = -5, d = 4$$

$$a =-5, d = -6$$

$$a = -5, d = -4$$

$$a = 5, d = -4$$

Solution

Question 4

No

Yes, $$d=8$$

Yes, $$d=-8$$

Yes, $$d=9$$

Solution

Question 5

Common difference: $$2$$ and Other three terms are: $$32, 64, 128$$

Common difference: $$4$$ and Other three terms are: $$24, 32, 40$$

Common difference: $$8$$ and Other three terms are: $$20, 24, 28$$

None of these

Solution

Question 6

$$a =$$ $$\sqrt{2}$$$$, d=$$ $$\sqrt{4}$$

$$a =$$ $$\sqrt{2}$$$$, d=$$ $$\sqrt{2}$$

Its not an AP

None of these

Solution

Question 7

$$a=2$$; $$d=\dfrac{1}{2}$$; other terms $$4,$$ $$\dfrac{9}{2},5$$

$$a=3$$; $$d=\dfrac{1}{2}$$; other terms $$6, 8, 10$$

$$a=2$$; $$d=\dfrac{3}{2}$$; other terms $$7, 8, 15$$

$$a=3$$; $$d=\dfrac{3}{2}$$; other terms $$4, 5, 15$$

Solution

Question 8

First term: $$-3$$ and Common difference: $$2$$

First term: $$-1$$ and Common difference: $$-3$$

First term: $$1$$ and Common difference: $$3$$

First term: $$3$$ and Common difference: $$-2$$

Solution

Question 9

The first four terms of the AP are $$20, 40, 60, 80.$$

The first four terms of the AP are $$10, 20, 30, 40.$$

The first four terms of the AP are $$15, 30, 45, 60.$$

Data insufficient

Solution

Question 10

First term: $$7$$ and Common difference: $$7$$

First term: $$3$$ and Common difference: $$-1$$

First term: $$-5$$ and Common difference: $$4$$

First term: $$3$$ and Common difference: $$-2$$

Solution

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