Question 40 of 51intermediate🔧 ApplyNumerical4 marks

How many multiples of 4 lie between 10 and 250?

Correct Answer

60

Exercise: END-OF-CHAPTER EXERCISES | Q: 4 | (Page 22)
For More Understanding

Explanation

The question requires finding the number of multiples of 4 between 10 and 250. As per the textbook hint, these multiples form an Arithmetic Progression (AP). The smallest multiple of 4 greater than 10 is 12, and the largest multiple of 4 less than 250 is 248. Using the nth term formula of an AP, we can calculate the total number of terms in this sequence.

Solution Steps

  1. Step 1: Find the smallest and largest multiples of 4 between 10 and 250. Smallest multiple = 12, Largest multiple = 248.

  2. Step 2: Form the AP. The sequence is 12, 16, 20, ..., 248. Here, first term (a) = 12, common difference (d) = 4, and last term (a_n) = 248.

  3. Step 3: Apply the nth term formula of an AP: a_n = a + (n - 1)d. Substituting the values: 248 = 12 + (n - 1)4.

  4. Step 4: Solve for n. 248 - 12 = (n - 1)4 => 236 = (n - 1)4 => n - 1 = 59 => n = 60.

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