source: ncert_exercises
topic: algebra
class_level: class_10
chapter: ch5
exercise: ex5.1
difficulty: beginner
Class 10 | Ch5: Arithmetic Progressions | Exercise 5.1
AP: Sequence where difference between consecutive terms is constant. Common difference d = a₂-a₁ = a₃-a₂ = ... General form: a, a+d, a+2d, ...
Q1. In which of the following situations, does the list of numbers form AP? (i) Taxi fare after each km when fare is ₹15 for 1st km and ₹8 for each additional km. (ii) Amount of air in a cylinder when a vacuum pump removes 1/4 of air remaining each time. (iii) Cost of digging a well after each metre if it costs ₹150 for first metre and rises ₹50 for each subsequent metre. (iv) Amount of money in the account every year when ₹10000 is deposited at compound interest at 8% p.a. Answer: (i) Fares: 15, 23, 31, 39... d=8 constant. YES, AP. ✅ (ii) Each time removes 1/4, so remaining: V, 3V/4, 9V/16... ratio is constant → geometric, NOT AP. ✅ (iii) Costs: 150, 200, 250... d=50. YES, AP. ✅ (iv) Compound interest: not constant difference → NOT AP. ✅
Q2. Write first four terms of AP when first term a and common difference d are: (i) a=10, d=10 (ii) a=-2, d=0 (iii) a=4, d=-3 (iv) a=-1, d=1/2 (v) a=-1.25, d=-0.25 Answer: (i) 10,20,30,40. ✅ (ii) -2,-2,-2,-2. ✅ (iii) 4,1,-2,-5. ✅ (iv) -1,-1/2,0,1/2. ✅ (v) -1.25,-1.50,-1.75,-2.00. ✅
Q3. For the following APs, write first term and common difference: (i) 3,1,-1,-3 (ii) -5,-1,3,7 (iii) 1/3,5/3,9/3,13/3 (iv) 0.6,1.7,2.8,3.9 Answer: (i) a=3, d=-2. ✅ (ii) a=-5, d=4. ✅ (iii) a=1/3, d=4/3. ✅ (iv) a=0.6, d=1.1. ✅
Q4. Which of the following are APs? If so, find common difference d: (i) 2,4,8,16 (ii) 2,5/2,3,7/2 (iii) -1.2,-3.2,-5.2,-7.2 (iv) -10,-6,-2,2 (v) 3,3+√2,3+2√2,3+3√2 (vi) 0.2,0.22,0.222 (vii) 0,-4,-8,-12 (viii) -1/2,-1/2,-1/2 (ix) 1,3,9,27 (x) a,2a,3a,4a (xi) a,a²,a³,a⁴ Answer: (i) Differences:2,4,8 — not constant. NOT AP. ✅ (ii) d=1/2. YES AP. ✅ (iii) d=-2. YES AP. ✅ (iv) d=4. YES AP. ✅ (v) d=√2. YES AP. ✅ (vi) 0.02,0.002 — not constant. NOT AP. ✅ (vii) d=-4. YES AP. ✅ (viii) d=0. YES AP. ✅ (ix) Differences:2,6,18 — not constant. NOT AP. ✅ (x) d=a. YES AP. ✅ (xi) a(a-1),a²(a-1)— not constant. NOT AP. ✅