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Question
How many numbers lie between 10 and 300, which when divided by 4 leave a remainder 3?
Solution
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 ...[∵ nth term, an = a + (n – 1)d]
⇒ 299 = 11 + (n – 1)4
⇒ 299 – 11 = (n – 1)4
⇒ 4(n – 1) = 288
⇒ (n – 1) = 72
∴ n = 73
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