Maths · Algebra · chapter 5 of 14
Class 10 Maths Chapter 5: Arithmetic Progressions Assertion-reason questions with answers
2 assertion-reason questions on Arithmetic Progressions, each with its answer and the reason, written from the NCERT chapter. Open a question's solution to check your working; then take the free test to find your next chapter. Each question gives an Assertion (A) and a Reason (R); choose how they stand to each other.
Question 1
Assertion (A): The values of a scooter that loses 10% of its value every year, recorded at the end of each year, form an AP. Reason (R): In an AP each term after the first is obtained by adding a fixed number to the preceding term.
Show answer
Answer: (d) A is false, but R is true.
R is the definition of an AP and is true. A is false: losing 10% of the value each time multiplies by 0.9, so the yearly fall shrinks (for ₹50,000: ₹5,000, then ₹4,500, . . .) and the differences are not fixed.
Question 2
Assertion (A): The 10th term of the AP 2, 9, 16, . . . is 65. Reason (R): The nth term of an AP is aₙ = a + (n − 1)d.
Show answer
Answer: (a) Both A and R are true, and R is the correct explanation of A.
a₁₀ = 2 + 9 × 7 = 65, worked straight from R. Both true and R explains A.