Question

How many numbers are there between 200 and 500 which is divisible by 4

Answer 1

Answer:-

• Sequence of numbers which are divisible by 4 between 200 and 500 is 204 , 208 , 212 ... , 496.

If we assume that this sequence is in AP,

• a (first term) = 204

• d (common difference) = 208 - 204 = 4

• nth term – a(n) = 496.

We know that,

nth term of an AP = a + (n - 1)d

→ 496 = 204 + (n - 1)(4)

→ 496 = 204 + 4n - 4

→ 496 - 204 + 4 = 4n

→ 296 = 4n

→ 296/4 = n

→ n = 74

Hence, there are 74 numbers between 200 and 500 which are divisible by 4.

Additional Information:-

• A series in each term (except first term) differs from its preceding term by a fixed quantity is called an Arithmetic Progression (AP).

• The fixed quantity is called common difference.

• General form of an AP is a , a + d..,if a is the first term and d is the common difference.

• nth term of an AP = a + (n - 1)d

• Sum of first n terms = n /2 * [ 2a + (n - 1)d ] (or) n/2 (a + l) where l is the last term or nth term.