Find the number of terms in each of the following APs:
i) 7, 13, 19,..., 205
ii) 18, 15 ½, 13 ,..., -47

Solution:

The formula for n^th term of an AP is aₙ = a + (n - 1) d

Here, aₙ is the n^th term, a is the first term, d is the common difference and n is the number of terms.

(i) 7, 13, 19,..., 205

a = 7

d = 13 - 7 = 6

aₙ = 205

n = ?

aₙ = a + (n - 1)d

a + (n - 1)d = 205

7 + (n - 1) 6 = 205

(n - 1) 6 = 205 - 7

(n - 1) 6 = 198

n - 1 = 33

Number of terms in the given Arithmetic Progression is 34.

ii) 18, 15 ½, 13 ,..., -47

a = 18

aₙ = -47

n = ?

d = 15 ½ - 18

= 31/2 - 18

= - 5/2

aₙ = a + (n - 1)d

- 47 = a + (n - 1) d

- 47 = 18 + (n - 1) (- 5 / 2)

- 65 = (- 5/2) n + 5 / 2

5/2 n = 5/2 + 65

5/2 n = 135 / 2

n = (135 / 2) × (2 / 5)

= 27

The number of terms in the given AP is 27.

☛ Check: Class 10 Maths NCERT Solutions Chapter 5

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Video Solution:

Find the number of terms in each of the following APs: i) 7, 13, 19,..., 205 ii) 18, 15 ½, 13 ,..., -47

NCERT Solutions Class 10 Maths Chapter 5 Exercise 5.2 Question 5

Summary:

The number of terms in the APs 7, 13, 19,……,205 and 18, 15½, 13,…,−47 are 34 and 27 respectively.

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