Arithmetic Progressions Test

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Arithmetic Progressions Test - 25

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Weekly Quiz Competition

Question 1
1 / -0

If $$\displaystyle l=20,d=-1,n=17$$ , then the first term is :

A
$$30$$

B
$$32$$

C
$$34$$

D
$$36$$

Solution

Given $$l = 20, d = -1, n = 17$$
We need to find $$a$$.
By using $$l=a+(n-1)d$$
$$\therefore 20=a+(17-1)(-1)$$
$$20=a-16$$
$$a=20+16$$
$$\therefore a=36$$
Question 2
1 / -0

$$50^{th}$$ term of the AP. $$2, 5, 8, 11,.....$$ is :

A
$$147$$

B
$$149$$

C
$$151$$

D
$$153$$

Solution

Given series $$\displaystyle 2,5,8,11,.....$$ is in A.P.
$$\therefore \displaystyle a=2,d=3$$
We need to find $$50^{th}$$ term.
$$\therefore n=50$$
$$\therefore \displaystyle { a }_{ 50 }=a+49d$$
$$=2+49\left( 3 \right) $$
$$=2+147$$
$$=149$$
Question 3
1 / -0

Find the sum of the following APs: $$-37, -33, -29, .....$$ to $$12$$ terms

A
-180

B
180

C
200

D
-200

Solution

Here, $$a=-37, d=4$$ and $$n=12$$
Here we use the formula as given below:
$$S_n = \dfrac{n}{2}[2a+(n-1)d]$$
$$\therefore S_{12}=\dfrac {12}{2}(2\times -37+4\times 11)=6\times -30=-180$$
Question 4
1 / -0

Find the sum of the following APs: $$2, 7, 12, ......,$$ to $$10$$ terms

A
245

B
345

C
276

D
250

Solution

$$S=\dfrac {n}{2}(2a+d(n-1))$$

Here, $$a=2, d=5$$ and $$n=10$$

$$Sum=\dfrac {10}{2}(2(2)+45)$$

$$=5\times 49=245$$
Question 5
1 / -0

In an AP, the $$9th$$ term is $$-72$$. The $$10th$$ term is $$60$$ less than the $$4th$$ term. Find the first term of the AP

A
$$8$$

B
$$-8$$

C
$$-152$$

D
$$10$$

Solution

Given that:
$$a_9=-72$$ and $$a_{10}=a_4-60$$
Let $$a$$ be the first term and $$d$$ be the common difference then
$$a+8d=-72$$ ......(1)
And
$$a+9d=a+3d-60$$
$$\Rightarrow 6d=-60\Rightarrow d=-10.$$
Substituting this value in equation (1), we get
$$a+8\times (-10)=-72$$
$$a=80-72$$
$$a=8$$

Hence,
The first term is $$8.$$
Question 6
1 / -0

Find the sum of the following APs: $$0.6, 1.7, 2.8, ......$$ to $$100$$ terms

A
5475

B
5505

C
6589

D
3844

Solution

Here $$a=0.6, d=1.1$$ and $$n=100$$
As we know, $$S_n = \dfrac {n}{2}[2a+(n-1)d]$$
$$\therefore S_{100}=\dfrac {100}{2} (2(0.6)+1.1\times 99)=50\times 110.1=5505$$
Question 7
1 / -0

The first term of an AP is $$-50$$ and the $$50th$$ term is $$48$$. Find the common difference

A
$$4$$

B
$$1$$

C
$$-3$$

D
$$2$$

Solution

Given,
First term $$ a = -50 $$

$$ 50^{th} $$ term, $$ T_{50} = 48 $$

$$ d = ? $$

$$ \boxed {T_{n} = a+(n-1)d} $$

$$ T_{50} = 48 $$

$$ 48 = -50+(50-1)d $$

$$ 48 = -50+49d $$

$$ 49d = 98 $$

$$ \boxed {d = 2} $$
Question 8
1 / -0

The value obtained by subtracting the $$10^{th}$$ term of an AP from the $$17^{th}$$ term is $$56$$. Find the common difference.

A
$$7$$

B
$$16$$

C
$$9$$

D
$$8$$

Solution

In an Arithmetic Progression the general term of an A.P. is given by $$T_n$$:
$$ \boxed {T_{n} = a+(n-1)d} $$
According to the statement:
$$ T_{17}-T_{10} = 56 $$
$$ a+(17-1)d-[a+(10-1)d] = 56 $$
$$ a+16d-[a+9d] = 56 $$
$$ a+16d-a-9d = 56 $$
$$ 7a = 56 $$
$$\boxed {d = 8} $$
Question 9
1 / -0

The common difference of the sequence $$5,8,11,14,$$ is

A
$$3$$

B
$$-3$$

C
$$0$$

D
$$1$$

Solution

Given, $$5,8,11,14$$
$$\therefore 8-5=3$$
$$11-8=3$$
$$14-11=3$$
The common difference of the sequence $$5,8,11,14$$ is $$3$$
Question 10
1 / -0

In an AP, the $$4th$$ term is $$36$$. The $$21st$$ term is $$108$$ more than the $$9th$$ term. Find the common difference.

A
$$12$$

B
$$9$$

C
$$4$$

D
$$-3$$

Solution

Given: $$ T_{4} = 36 $$
$$ T_{21} = 108+T_{9} $$
$$ d = ? $$
General term of an A.P. $$=T_{n} = a+(n-1)d $$
$$T_{21} = 108+T_{9} $$
$$ a+(21-1)d = 108+a+(9-1)d $$
$$ 20d = 108 +8d $$
$$ 12d = 108 $$
$$ \boxed {d = 9} $$

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Re-Attempt Weekly Quiz Competition

Arithmetic Progressions Test - 25

Result

Arithmetic Progressions Test - 25

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SHARING IS CARING

Question 1

$$30$$

$$32$$

$$34$$

$$36$$

Solution

Question 2

$$147$$

$$149$$

$$151$$

$$153$$

Solution

Question 3

-180

180

200

-200

Solution

Question 4

245

345

276

250

Solution

Question 5

$$8$$

$$-8$$

$$-152$$

$$10$$

Solution

Question 6

5475

5505

6589

3844

Solution

Question 7

$$4$$

$$1$$

$$-3$$

$$2$$

Solution

Question 8

$$7$$

$$16$$

$$9$$

$$8$$

Solution

Question 9

$$3$$

$$-3$$

$$0$$

$$1$$

Solution

Question 10

$$12$$

$$9$$

$$4$$

$$-3$$

Solution

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