Arithmetic Sequence

Q.

The angles of a triangle are in A.P. If the greatest angle is three times the smallest angle, find the greatest angle in the triangle.

1. ${80}^{\circ }$

2. ${75}^{\circ }$

3. ${100}^{\circ }$

4. ${90}^{\circ }$

Q. Question 1 (iii)
In which of the following situations does the list of numbers involved make an arithmetic progression and why?
(iii) The cost of digging a well after every metre of digging, when it costs Rs. 150 for the first metre and rises by Rs. 50 for each subsequent metre.

Q.

Question 5
What can the maximum number of digits be in the repeating block of digits in the decimal expansion of $\frac{1}{17}$? Perform the division to check your answer.

Q.

In each of the arithmetic sequences below, some numbers are missing. Their positions are marked with a. Find these numbers.

Q. If $p,q,r$ and $s$ are in AP, then which of the following is true?

1. $p-q=s-r$
2. $p+q+r+s=0$
3. $p+q=r+s$
4. $q-p=s-r$

Q.

Let AP $(a;d)$denote the set of all the terms of an infinite arithmetic progression with first term $a$ and common difference$d>0$. If $AP(1;3)\cap AP(2;5)\cap AP(3;7)=AP(a;d)$ then $a+d$ equals:

Q.

For what value of n, 5ⁿ ends with a zero

1. Any integer

2. Any real number

3. Any even number

4. Never ends with a zero

Q.

How many four digit numbers are there such that when they are divided by 101 they have 99 as remainder?

Q.

What is meant by common difference? Examples of common difference

Q. What is the value of X for which the expression (2x) n ends with 0 , where n is any natural number and x is a non zero digit

Q. If the first term of an AP is 4 and the common difference is -4, then the $5^{th}$ term will be .

1. 12
2. -12
3. -8
4. 4

Q.

The number of terms from 1 to 1000 divisible by 7 are

1. 142

2. 143

3. 141

4. 144

Q. Find all the possible pairs of two natural numbers whose sum is 77 and their g.c.d is 7

Q.

The first term of an arithmetic sequence is 6 and common difference is 4. Then the algebraic expression for sum of the first 'n' terms its.

1. $2n+4n^2$

2. $2+4n^2$

3. 2+4n

4. $2n^2+4n$

Q.

Missing terms in the arithmetic sequence are 2, 6, 10, 14, ___, ___, ___, 30.

1. 16, 18, 20

2. 18, 22, 26

3. 19, 20, 21

4. 17, 19, 21

Q. Write the sequence obtained by adding two consecutive natural numbers starting from 1. Is this an arithmetic sequence?

1. 1, 4, 7, 10, ... ; Yes
2. 3, 5, 7, 9, ... ; Yes
3. 3, 5, 7, 9, ... ; No
4. 1, 3, 5, 8, ... ; No

Q.

Justify if the series $\sqrt{3},\sqrt{12},\sqrt{27},\sqrt{48},...$ form an AP ?

Q.

What is empty set?

Q. Which of the following are arithmetic progressions?

1. 2, 3, 4, 5…..
2. 9, 8, 7, 6….
3. 0, 1, 4, 9....
4. 0, 0, 0, 0....

Q. Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.
(i) 2, 4, 8, 16, …
(ii) $2,\frac{5}{2},3,\frac{7}{2},\dots$
(iii) -1.2, -3.2, -5.2, -7.2 …
(3 Marks)

Q.

The angles of a triangle are in A.P. If the greatest angle is twice the least, find the greatest angle.

1. ${60}^{\circ }$

2. ${80}^{\circ }$

3. ${40}^{\circ }$

4. ${100}^{\circ }$

Q. Choose the correct answer in each of the following questions:

The common difference of the AP $\frac{1}{p},\frac{1-p}{p},\frac{1-2p}{p},...$ is [CBSE 2013]

(a) p (b) −p (c) −1 (d) 1

Q. 513 = n/2 { 108+( n-1)(-3)} . Find n.

Q.

In which of the following situations , does the list of numbers involved make an arithmetic progression , and why?

4) The amount of money in the account every year , when Rs.10, 000 is deposited at compound interest at 8%/annum.

Q.

Which of the following represents a sequence obtained by starting with any number and adding a fixed number repeatedly?

1. Arithmetic mean

2. Arithmetic sequence

3. Ordered Sequence

4. None of the above

Q.

A sequence formed by adding 5 to each number starting from 1 is an arithmetic sequence.

1. False

2. True

Q. Which of the following sequences is/are in arithmetic progression?

1. $0,\frac{1}{2},1,\frac{3}{2},2$
2. $1,4,9,16,25$
3. $-\sqrt{2},0,\sqrt{2},2\sqrt{2},3\sqrt{2}$
4. $5,10,20,35,55$

Q.

The H.C.F and L.C.M. of the two expression are (m − 3) and (m³ + m² − 17m + 15) respectively. Find the expressions.

Q.

What is induction method used in real numbers

Q.

Sum of three consecutive terms in an AP is 15 and their product is 0. The sequence is?

1. 0, 5, 10.

2. 10, 5, 0.

3. Both a and b are correct.

4. None of these.