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

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

Question:

Find the number of terms in each of the following APs : 7, 13, 19, . . . , 205

Given:

Arithmetic Progression (AP): 7, 13, 19, ..., 205

To Find:

The number of terms (n) in the given AP.

Formula:

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

Solution:

Here, 

the first term is a = 7, 

the common difference is d = 13 - 7 = 6, and 

the last term is an = 205.

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

205 = 7 + (n - 1)6

⇒ 205 - 7 = (n - 1)6

⇒ 198 = (n - 1)6

⇒ 198 6 = n - 1

⇒ 33 = n - 1

⇒ n = 33 + 1

⇒ n = 34

Result:

Therefore, the number of terms in the given AP is 34.

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