Question

Find the sum of all natural numbers between 200 and 1502 which are exactly divisible by 3.

Answer 1

Answer:

138024

Step-by-step explanation:

Step 1: Everyday activities include the use of numbers. Numerols are a common name for them. Without numbers, we are unable to count items, dates, hours, money, etc. These numerals are sometimes used for labelling and occasionally for measuring. Numbers are able to execute mathematical operations on them due to their inherent characteristics. Both quantitative and verbal expressions of these quantities are available.

Step 2: When two or more numbers or quantities are joined together, the total number or sum is: 13 plus 8 add up to 21. Synonyms, antonyms, and instances in a thesaurus. to multiply numbers.

Step 3: The AP. for such numbers is 208,216,224,.................1496

Hence, a = 208

          d = 8

Let there be n numbers so, an = 1496

so, 208 + (n-1)8 = 1496

 Hence, n = 162

∴ Required sum = S162 = 162*(208+1496)/2 =  138024

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Answer 2

The sum of all natural numbers between 200 and 1502 which is exactly divisible by 3 is 368,900.

To find the sum of all natural numbers between 200 and 1502 that are exactly divisible by 3, we can use the formula for the sum of an arithmetic series. An arithmetic series is a sequence of numbers where the difference between consecutive terms is constant.

Let's call the first term "a" and the common difference "d". We can use the formula for the number of words in an arithmetic series, n, to calculate the last time:

n = (1502 - 200) ÷ d + 1

Since we want to find numbers that are exactly divisible by 3, we can set the common difference, d, equal to 3.

n = (1502 - 200) ÷ 3 + 1 = 1300 ÷ 3 + 1 = 433 + 1 = 434

The last term can be found by multiplying the common difference by the number of terms minus 1 and adding the first term:

b = a + (n - 1)d

b = 200 + (434 - 1) × 3 = 200 + 1300 = 1500

So, the last term is 1500 and the first term is 200.

Using the formula for the sum of an arithmetic series, we can now find the sum of all numbers between 200 and 1502 that are exactly divisible by 3:

S = (n ÷ 2) × (a + b)

S = (434 ÷ 2) × (200 + 1500) = 217 × 1700 = 368900

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