Arithmetic Progressions Test

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Arithmetic Progressions Test - 31

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Question 1
1 / -0

Find the sum of the first $$25$$ terms of an A.P whose $$n$$th term is given by $${a}_{n}=2-3n$$.

A
$$-925$$

B
$$-928$$

C
$$-923$$

D
$$-929$$

Solution

$$a_{n}=2-3n$$

$$a_{1}=-1$$

$$a_{2}=-4$$

$$d=-4+1=-3$$

$$S_{25}=\dfrac{25}{2}[-2+24(-3)]=-925$$

Hence, option A is correct.
Question 2
1 / -0

If two terms of an arithmetic progression are known, which values need to be determined to form the entire arithmetic progression?

A
If $$a$$ and $$d$$ can be found out.

B
If $$a$$ and $$n$$ can be found out.

C
If $$n$$ and $$d$$ can be found out.

D
If $$t_n$$ and $$n$$ can be found out.

Solution

If two terms of an arithmetic progression, then the two terms can be represented using $$t_n = a + (n_1-1)d$$ and $$a + (n_2-1)d$$. These two equations can be solved for finding the values of '$$a$$' and '$$d$$'.
The arithmetic progression can be formed after the values of a and d are known.
Question 3
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The first term and the common difference of the arithmetic progression $$3,10,17,24,...$$ is?

A
$$7$$ and $$3$$

B
$$3$$ and $$7$$

C
$$3$$ and $$10$$

D
Not defined

Solution

The first term of the arithmetic progression $$3,10,17,24,...$$ is $$3$$. The common difference or the difference between its consecutive terms is $$t_2-t_1=10-3=7$$. Also, $$t_3-t_2=17-10=7$$ Thus the correct answer is option '$$b$$'.
Question 4
1 / -0

The first term of an $$AP$$ whose $$6^{th}$$ terms is $$5$$ and the $$10^{th}$$ terms is $$9$$ is ____________.

A
$$4$$

B
$$10$$

C
$$0$$

D
$$6$$

Solution

The gernal form of A.P is $$a_n=a+(n-1)d$$
$$5=a+(6-1)d=a+5d$$
$$9=a+(10-1)d=a+9d$$
solving the two we get
$$d=1$$
$$a+5*1=5$$
$$a=0$$
Question 5
1 / -0

An arithmetic progression is defined as a sequence that has a fixed _______ between its two consecutive numbers.

A
difference

B
ratio

C
sum

D
Cant say

Solution

An arithmetic progression is a sequence of numbers that has a fixed difference between its two consecutive numbers. Thus the correct answer is option '$$a$$'.
Question 6
1 / -0

What is the common difference in the arithmetic progression $$2,7,12,17,...$$?

A
$$6$$

B
$$5$$

C
$$7$$

D
$$9$$

Solution

The common difference in the arithmetic progression $$2,7,12,17,...$$ is the difference between its two consecutive terms.
The difference between its two consecutive terms here is $$7-2=5$$, or $$12-7=5$$ and so on.

Thus, the common difference is $$5$$.
Question 7
1 / -0

If any one term of an arithmetic progression along with the position of the term in the A.P. and the common difference are known, then which of the following can be found out.

A
The first term.

B
The term before the known term.

C
The term after the known term.

D
All of the above.

Solution

When one term of the arithmetic progression is known along with the common difference, then using that value of the common difference, the terms before and after the known term can be found out. Also substituting the values for $$d, n$$(the position of the term in the A.P. is known) and tn are known, then the value for a or the first term can be found out using the formula $$t_n = a + (n-1)d$$.
Question 8
1 / -0

The sum of $$n$$ terms of an A.P. is dependent on which of the following parameters?

A
Only $$a$$ and $$d$$.

B
Only $$n$$ and $$d$$.

C
$$a, n$$ and $$d$$.

D
Only $$a$$ and $$n$$.

Solution

The sum of n terms of an arithmetic progression is dependent on the first term '$$a$$', the common difference, d and the number of terms n as the formula is given as $$S_n$$ $$ = \dfrac{n}{2} (2a+(n-1)d)$$
Thus the correct answer is '$$c$$'.
Question 9
1 / -0

$$\sqrt{8},\sqrt{18},\sqrt{32}$$ are in AP. Find the next term and common difference.

A
$$\sqrt {50}, \sqrt 2$$

B
$$\sqrt {55}, 2$$

C
$$\sqrt {48}, \sqrt 2$$

D
None

Solution

$$c.d.\>=\>\sqrt{18}-\sqrt8=3\sqrt2-2\sqrt2=\sqrt2\\\therefore\>next\>term\>=\>\sqrt{32}+\sqrt2\\=4\sqrt2+\sqrt2=5\sqrt2=\sqrt{50}$$
Question 10
1 / -0

Chose the correct option for the following sequence:
$$-25, -23, -21, -19..$$

A
is an $$A.P.$$ Reason $$d=3$$

B
is an $$A.P.$$ Reason $$d=2$$

C
is an $$A.P.$$ Reason $$d=4$$

D
is not an $$A.P.$$

Solution

$$-25,-23,-21,-19$$
Common difference$$=2$$
Hence series in AP

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Arithmetic Progressions Test - 31

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Arithmetic Progressions Test - 31

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Question 1

$$-925$$

$$-928$$

$$-923$$

$$-929$$

Solution

Question 2

If $$a$$ and $$d$$ can be found out.

If $$a$$ and $$n$$ can be found out.

If $$n$$ and $$d$$ can be found out.

If $$t_n$$ and $$n$$ can be found out.

Solution

Question 3

$$7$$ and $$3$$

$$3$$ and $$7$$

$$3$$ and $$10$$

Not defined

Solution

Question 4

$$4$$

$$10$$

$$0$$

$$6$$

Solution

Question 5

difference

ratio

sum

Cant say

Solution

Question 6

$$6$$

$$5$$

$$7$$

$$9$$

Solution

Question 7

The first term.

The term before the known term.

The term after the known term.

All of the above.

Solution

Question 8

Only $$a$$ and $$d$$.

Only $$n$$ and $$d$$.

$$a, n$$ and $$d$$.

Only $$a$$ and $$n$$.

Solution

Question 9

$$\sqrt {50}, \sqrt 2$$

$$\sqrt {55}, 2$$

$$\sqrt {48}, \sqrt 2$$

None

Solution

Question 10

is an $$A.P.$$ Reason $$d=3$$

is an $$A.P.$$ Reason $$d=2$$

is an $$A.P.$$ Reason $$d=4$$

is not an $$A.P.$$

Solution

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