Top of Form

## CHAPTER 1  REAL NUMBERS

Competency based questions on ARITHMETIC PROGRESSION chapter 5 , Assertion and Reason based questions for class 10 ARITHMETIC PROGRESSION chapter 5

## Assertion and Reason Questions

Directions

Each of these questions contain two statements Assertion (A) and Reason (R). Each of the questions has four alternative choices, any one of which is correct answer.

You have to select one of the codes (a ), (b ), (c ), (d ) given below

a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

c) Assertion (A) is true but Reason (R) is false.

d) Assertion (A) is false but Reason (R) is true.

## ARITHMETIC PROGRESSION

Question 1
Assertion: Sum of natural number from 1 to 100 is 5050
Reason: Sum of n natural number is n(n + 1)/2
Ans a

Question 2

Assertion: Sum of fist n terms in an A.P. is given by the formula:

Sn = 2n×[2a + (n−1)d]

Reason: Sum of first 15 terms of 2 + 5 + 8 ——- is 345.
Ans a

Question 3

Assertion: The constant difference between any two terms of an AP is commonly known as common difference

Reason: the common difference of 2, 4, 6, 8 this A.P. sequence is 2
Ans a

Question 4

Assertion: Arithmetic progression is a sequence of numbers in which the difference of any two adjacent terms is constant.

Reason: 4, 8, 12, 16 this sequence is an A.P.
Ans a

Question 5
Assertion: If numbers a, b, c are in A.P then b – a = c - b
Reason: given three numbers are in AP, then the common difference will be same.
Ans a

Question 6
Assertion: The sum of series with the nth term tn = (9 - 5n) is 220 when no. of terms n = 6
Reason : Sum of first n terms in an A.P. is given by the formula: Sn = 2n×[2a + (n−1)d]
Ans a

Question 7

Assertion: An AP containing a finite number of terms is called finite AP

Reason: 3, 5, 7, 9, 11, 13, 15, 17, 19, 21 is an finite AP
Ans a

Question 8

Assertion: the value of n, if a = 10, d = 5, an = 95.

Reason: the formula of general term an is an = a + (n - 1)d.
Ans a

Question 9

Assertion: Arithmetic between 5 and 90 is 47.5

Reason: Arithmetic between two given number a, b is (a + b)/2
Ans a

Question 10

Assertion: The 11th term of an AP is 7, 9, 11, 13_________is 67

Reason: if Sn is the sum of first n terms of an AP then its nth term an is given by an = Sn + Sn - 1
Ans a

Question 11
Assertion : If Sn is the sum of the first n terms of an A.P., then its nth term an is given by a= S– Sn–1.
Reason : The 10th term of the A.P. 5, 8, 11, 14, ................... is 35.

Question 12

Assertion: the value of n, if a = 10, d = 5, an = 95.

Reason: the formula of general term an is an = a + (n - 1)d.
Ans: (a)

Question 13
Assertion: The 11th term of an AP is 7, 9, 11, 13_________is 67
Reason: if Sn is the sum of first n terms of an AP then its nth term an is given by
an = Sn + Sn–1
Ans: (d)

Question 14

Assertion: The sum of the first n terms of an arithmetic progression is given by the formula Sn = n/2 [2a + (n - 1)d], where 'a' is the first term and 'd' is the common difference.

Reason: The formula for the sum of an arithmetic progression is derived from the formula for the nth term, which is given by an = a + (n - 1)d.
Ans: a

Question 15

Assertion: In an arithmetic progression, if the first term 'a' is 5 and the common difference 'd' is 3, then the nth term an is given by an = 5n + 3.

Reason: The nth term of an arithmetic progression is found by adding the common difference 'd' to the first term 'a' for 'n' times.
Ans d

1. Assertion and reason format is often used to justify statements logically. An assertion states a mathematical fact or claim, while the reason provides a logical explanation or proof for why the assertion is true. This format helps clarify reasoning processes and strengthens mathematical arguments by requiring explicit justification for assertions made. It's commonly utilized in proofs and problem-solving to ensure clarity and rigor in mathematical reasoning.