Question
Find the sum of all natural numbers less than 1000 that
are multiples of 3 but not of 5.Solution
Sum(multiples of 3 below 1000) − Sum(multiples of 15 below 1000). Multiples of 3 less than 1000: 3, 6, …, 999 This is an AP with a = 3, d = 3, last term l = 999 Number of terms: n₁ = 999/3 = 333 Sum S₁ = n₁/2 × (first + last) = 333/2 × (3 + 999) = 333/2 × 1002 = 333 × 501 = 166,833 Multiples of 15 less than 1000: 15, 30, …, 990 a = 15, d = 15, l = 990 n₂ = 990/15 = 66 Sum S₂ = 66/2 × (15 + 990) = 33 × 1005 = 33 × 1000 + 33 × 5 = 33,000 + 165 = 33,165 Required sum = S₁ − S₂ = 166,833 − 33,165 = 133,668.
Which dynasty constructed the Gol Gumbaz?
Which of the following is not the part of the AXIS power during the World War- II?
The First Europeans arrived in India were :
According to the excavated evidence, animal husbandry started-
Which of the following dynasty is also known as the Mamluk Dynasty?
Who coined the phrase "We divide and they rule" during the colonial period in India?
Who is known as DESHBANDHU?
The remains of an ancient civilization from around 4000 BC were discovered in:
Which of the following statements given below about the post-Mauryan period is correct?
The Quit India Movement was started after the failure of:
