Chapter 5 · Arithmetic Progressions

NCERT Class 10 Maths Exercise 5.1

All 4 questions of NCERT Class 10 Maths Exercise 5.1 (Arithmetic Progressions), in the book's order, each with its answer and a step-by-step solution.

1. Q1
   In which of the following ​situations does the list of numbers involved make an arithmetic progression, and why? ​

   1. (i)The taxi fare after each km when the fare is Rs $15$ for the first km and Rs $8$ for each additional km.
   2. (ii)The amount of air present in ​a ​cylinder when a vacuum pump removes $\frac{1}{4}$ of the air remaining in the cylinder at a time.
   3. (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.
   4. (iv)The amount of money in ​the account every year, when Rs $10000$ is ​deposited at compound interest at $8\%$ per annum.
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   (i) AP with $d=8$; (ii) Not an AP (air decreases by a constant factor $\frac{3}{4}$, so it is geometric); (iii) AP with $d=50$; (iv) Not an AP (balance grows by a constant factor $1.08$, so it is geometric).

   Step-by-step solution →
2. Q2
   Write the ​first four terms ​of ​the AP ​when the ​first term $a$ and the common difference $d$ are given as follows: ​

   1. (i)$a=10$, $d=10$
   2. (ii)$a=-2$, $d=0$
   3. (iii)$a=4$, $d=-3$ ​
   4. (iv)$a=-1$, $d=\frac{1}{2}$
   5. (v)$a=-1.25$, $d=-0.25$
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   (i) $10,20,30,40$; (ii) $-2,-2,-2,-2$; (iii) $4,1,-2,-5$; (iv) $-1,-\frac{1}{2},0,\frac{1}{2}$; (v) $-1.25,-1.5,-1.75,-2.0$.

   Step-by-step solution →
3. Q3
   For the following ​APs, write ​the ​first ​term and ​the ​common difference: ​

   1. (i)$3,1,-1,-3,\dots$
   2. (ii)$-5,-1,3,7,\dots$
   3. (iii)$\frac{1}{3},\frac{5}{3},\frac{9}{3},\frac{13}{3},\dots$
   4. (iv)$0.6,1.7,2.8,3.9,\dots$
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   (i) $a=3,d=-2$; (ii) $a=-5,d=4$; (iii) $a=\frac{1}{3},d=\frac{4}{3}$; (iv) $a=0.6,d=1.1$.

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4. Q4
   Which of the ​following ​are APs? If they ​form an AP, find the common difference $d$ and write ​three more terms. ​

   1. (i)$2,4,8,16,\dots$
   2. (ii)$2,\frac{5}{2},3,\frac{7}{2},\dots$
   3. (iii)$-1.2,-3.2,-5.2,-7.2,\dots$ ​
   4. (iv)$-10,-6,-2,2,\dots$
   5. (v)$3,3+\sqrt{2},3+2\sqrt{2},3+3\sqrt{2},\dots$
   6. (vi)$0.2,0.22,0.222,0.2222,\dots$
   7. (vii)$0,-4,-8,-12,\dots$
   8. (viii)$-\frac{1}{2},-\frac{1}{2},-\frac{1}{2},-\frac{1}{2},\dots$
   Show answer

   APs: (ii) $d=\frac{1}{2}$; (iii) $d=-2$; (iv) $d=4$; (v) $d=\sqrt{2}$; (vii) $d=-4$; (viii) $d=0$. Not APs: (i) And (vi).

   Step-by-step solution →