Chapter 1Chapter 2Chapter 3Chapter 4Chapter 5Chapter 6Chapter 7Chapter 8Chapter 9Chapter 10Chapter 11Chapter 12Chapter 13Chapter 14Chapter 15
Mathematics Chapter 5

Arithmetic Progressions

Exercise 5.1, 5.2, 5.3 with step by step solutions

Exercise 5.1 - Identify AP and find common difference

Q1. 2, 4, 6, 8, 10 ... Is it an AP? Find d.v

Consecutive differences: 4-2=2, 6-4=2, 8-6=2.

Difference is constant.

Final: Yes, AP with d=2.

Q2. 3, 7, 11, 15 ...v

Differences: 4,4,4.

Final: AP, d=4.

Q3. 5, 9, 15, 23 ...v

Differences: 4,6,8 (not same).

Final: Not an AP.

Q4. -1, -5, -9, -13 ...v

Differences: -4,-4,-4.

Final: AP, d=-4.

Q5. 0, 0, 0, 0 ...v

Each difference is 0.

Final: AP, d=0.

Exercise 5.2 - Find nth term

Q1. Find 10th term of AP: 2, 5, 8, 11, ...v

a=2, d=3, n=10.

Formula: a_n=a+(n-1)d.

a_10=2+9*3=2+27=29.

Final: 10th term = 29.

Q2. Find 15th term of AP: 7, 10, 13, 16, ...v

a=7, d=3.

a_15=7+14*3=49.

Final: 15th term = 49.

Q3. Which term of AP 3,8,13,18,... is 78?v

a=3, d=5.

a_n=3+(n-1)5=78.

5n-2=78 => 5n=80 => n=16.

Final: 78 is the 16th term.

Q4. Find nth term of AP 11, 8, 5, 2, ...v

a=11, d=-3.

a_n=11+(n-1)(-3)=11-3n+3=14-3n.

Final: a_n = 14 - 3n.

Q5. Is 100 a term of AP 6, 13, 20, 27, ...?v

a=6, d=7.

6+(n-1)7=100 => 7n-1=100 => 7n=101.

n is not integer.

Final: 100 is not a term of this AP.

Exercise 5.3 - Sum of n terms

Q1. Find sum of first 20 terms of AP: 3,7,11,...v

a=3, d=4, n=20.

S_n=n/2[2a+(n-1)d].

S_20=20/2[6+19*4]=10[6+76]=820.

Final: S_20 = 820.

Q2. Find sum of first 30 natural numbers.v

AP: 1,2,3,...,30 so a=1, l=30, n=30.

S_n=n/2(a+l)=30/2(31)=15*31=465.

Final: 465.

Q3. Sum of first 25 odd numbers.v

AP: 1,3,5,... with a=1, d=2, n=25.

S_25=25/2[2+24*2]=25/2(50)=625.

Final: 625.

Q4. Find n if S_n of AP 5,8,11,... is 405.v

a=5,d=3.

S_n=n/2[10+3(n-1)] = n/2(3n+7)=405.

n(3n+7)=810 -> 3n^2+7n-810=0.

Factor: (n-15)(3n+54)=0.

Final: n = 15.

Q5. Which AP has sum of first n terms n^2+2n?v

Given S_n=n^2+2n.

a_n=S_n-S_(n-1).

S_(n-1)=(n-1)^2+2(n-1)=n^2-1.

a_n=(n^2+2n)-(n^2-1)=2n+1.

So terms are 3,5,7,9,...

Final: AP is 3, 5, 7, 9, ...

Chapter 5 step-by-step solutions added.

Continuing chapter by chapter.

Next Chapter: Triangles ->

NCERT Class 10 Maths - Chapter 5