Chapter 10 · ICSE Class 10 Mathematics (Selina Concise)

Arithmetic Progression

Find terms and sums of arithmetic progressions, where each term increases by a constant common difference.

➕ Chapter 10

The arithmetic progression 5, 9, 13, 17 with the common difference of 4 shown between each pair Four terms of an arithmetic progression, 5, 9, 13, 17, with arrows labeled plus 4 showing the constant common difference between consecutive terms 5 9 13 17 +4 +4 +4 a = 5, d = 4
10.1

The nth Term of an AP

In an AP, aₙ=a+(n−1)d, where a is the first term and d is the common difference.

1

Find the 10th term of the AP 3, 7, 11, 15, ...

a=3, d=4; a₁₀=3+9×4=39

2

Find the common difference if the 5th term of an AP is 17 and the first term is 5.

17=5+4d; 12=4d; d=3

10.2

Sum of an AP

Sₙ=n/2×[2a+(n−1)d], or equivalently Sₙ=n/2×(a+l) where l is the last term.

1

Find the sum of the first 10 terms of the AP 3, 7, 11, 15, ...

S₁₀=10/2×[2×3+9×4]=5×[6+36]=5×42=210

2

Find the sum of the first 20 natural numbers.

S₂₀=20/2×(1+20)=10×21=210

Practice

Exercises

1. Find the 15th term of the AP 2, 5, 8, 11, ...

2. Find d if the 8th term of an AP is 29 and the first term is 1.

3. Find the sum of the first 15 terms of the AP 2, 5, 8, 11, ...

4. Find the sum of the first 50 natural numbers.

5. How many terms of the AP 5, 9, 13, ... add up to 155?

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