Question

How many numbers lie between 10 and 300, which when divided by 4 leave a remainder 3?

Answer 1

Here, the first number is 11,

Which divided by 4 leave a remainder 3 between 10 and 300

Last term before 300 is 299,

Which divided by 4 leave remainder 3.

∴ 11, 15, 19, 23, 299

Here, first term (a) = 11,

Common difference (d) = 15 – 11 = 4   ...[∵ n^th term, a_n = a + (n – 1)d]

⇒ 299 = 11 + (n – 1)4

⇒ 299 – 11 = (n – 1)4

⇒ 4(n – 1) = 288

⇒ (n – 1) = 72

∴ n = 73