NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.2 Question 5(ii)

Question:

Find the number of terms in each of the following APs : 18, 15 1/2, 13, ... , -47

Given:

The given AP is 18, 1512, 13, ... , -47

To Find:

The number of terms in the given AP.

Formula:

The nth term of an AP is given by a_n = a + (n-1)d, where a is the first term, d is the common difference, and n is the number of terms.

Solution:

Here, 

a = 18, 

d = 1512 - 18 = -52, and 

a_n = -47.

Using the formula a_n = a + (n-1)d, we have:

-47 = 18 + (n-1)(-52)

⇒ -47 - 18 = (n-1)(-52)

⇒ -65 = (n-1)(-52)

⇒ n - 1 = 655/2 = 26

⇒ n = 26 + 1

⇒ n = 27

Therefore, the number of terms in the AP is 27

Result:

The number of terms in the given AP is 27.

Next question solution:

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.2 Question 6

Explore more in Arithmetic Progressions chapter:

Click this link to explore more NCERT Class X Chapter 5 Arithmetic Progressions solutions

Explore more:

Click this link to explore more NCERT Class X chapter solutions

© Kaliyuga Ekalavya. All rights reserved.