NCERT Class X Chapter 5: Arithmetic Progression Example 4

NCERT Class X Chapter 5: Arithmetic Progression Example 4

Question:

Which term of the AP : 21, 18, 15, . . . is – 81? Also, is any term 0? Give reason for your answer.

Given:

Arithmetic Progression (AP): 21, 18, 15, ...

To Find:

The term that is equal to -81 and whether any term is 0.

Formula:

nth term of an AP: an = a + (n-1)d, 

where, 

a is the first term and 

d is the common difference.

Solution:

Here, 

the first term a = 21 and 

the common difference d = 18 - 21 = -3.

Let the nth term be -81. 

Then, -81 = 21 + (n-1)(-3) 

⇒ -81 = 21 -3n + 3 

⇒ -81 = 24 -3n 

⇒ 3n = 105 

⇒ n = 1053 = 35

Therefore, the 35th term is -81.

To check if any term is 0, let an = 0. 

Then,

0 = 21 + (n-1)(-3) 

⇒ 3(n-1) = 21 

⇒ n-1 = 7 

⇒ n = 8.

Thus, the 8th term is 0.

Result:

The 35th term is -81. The 8th term is 0.

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