The Sum Of 333 Consecutive Odd Numbers Is 183183183. (2024)

FAQs

What three consecutive odd numbers have a sum of 333? ›

Answer. Which means that the first number is 110, the second number is 110 + 1 and the third number is 110 + 2. Therefore, three consecutive integers that add up to 333 are 110, 111, and 112.

Final answer:

The second number in the sequence is 61.

Expert-Verified Answer

The three consecutive odd integers that sum to 3 are -1, 1, and 3. They can be arrived at by setting up and solving the equation for consecutive odd integers, x + (x + 2) + (x + 4) = 3.

x + x + 3 + x + 6 = 333.

⇒ 3x = 324. ⇒ x = 324/3. ⇒ x = 108.

So the numbers are 60,61,62.

Odd Consecutive Integer Formula

If 2n + 1 is an odd integer, (2n + 3) and (2n + 5) will be the next two odd consecutive integers. For example, let 2n + 1 be 7, which is an odd integer. We find its consecutive integers as (7 + 2) and (7 + 4), or 9 and 11.

∴ so, the three numbers are 61,63 and 65.

Sum of n Odd Numbers Formula

Therefore, the series of odd numbers form an arithmetic progression. The sum of n odd numbers formula is described as follows, Sum of n odd numbers = n² (we will prove this in the next section) where n is a natural number and represents the number of terms.

Thus, the three consecutive odd natural numbers are 21, (21+2) and (21+4), i.e. 21, 23, and 25. Out of these, Only 23 is the prime number.

The total of any set of sequential odd numbers beginning with 1 is always equal to the square of the number of digits, added together. If 1,3,5,7,9,11,…, (2n-1) are the odd numbers, then; Sum of first odd number = 1.

What is the sum of 3 consecutive odd natural numbers always divisible by? ›

∴ Sum of three consecutive odd numbers is always divisible by 3.

So the numbers are 13,15,19. The sum of three odd consecutive numbers is 45 find the numbers.

Let the three consecutive odd numbers are x,x+2,x+4. According to question, The sum of three consecutive odd numbers is 33. Therefore, The numbers are 9,11 and 13.

1 Expert Answer

To find the sum of two numbers, we have to find two numbers that when added together give us the value 333. The problem also tells us that the numbers differ by a value of 1 since they are pages "on the same page". So, there you have it, Page 1 is 166 and page 2 is 167, which together add to 333.

The sum of these numbers is indeed 131 + 133 + 135 = 399. Therefore, the three consecutive odd numbers are 131, 133, and 135.

Hence, the three consecutive numbers are 10, 11, 12.