NCERT Class X Chapter 5: Arithmetic Progression Example 6

Question:

Check whether 301 is a term of the list of numbers 5, 11, 17, 23, . .

Given:

The list of numbers is 5, 11, 17, 23, . . .

To Find:

Whether 301 is a term of the given list of numbers.

Formula:

The nth term of an arithmetic progression is given by a_n = a + (n-1)d, 

where 

a is the first term and 

d is the common difference.

Solution:

The given list of numbers forms an arithmetic progression.

First term, a = 5

Common difference, d = 11 - 5 = 6

Let 301 be the nth term of the arithmetic progression. 

Then,

301 = 5 + (n - 1)6

⇒ 301 - 5 = (n - 1)6

⇒ 296 = (n - 1)6

⇒ n - 1 = 296 6

⇒ n - 1 = 49.333...

⇒ n = 50.333....

Since n must be an integer, 301 is not a term of the given arithmetic progression.

Result:

301 is not a term of the list of numbers 5, 11, 17, 23, . . .

Next question solution:

NCERT Class X Chapter 5: Arithmetic Progression Example 7.

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