Question

the sum of all natural numbers from 61 to 100 is​

Answer 1

Step-by-step explanation:

Let the numbers from 51 to 100 form an Arithmetic Progression or for a simpler word, a sequence.

The first term is 51 and the common difference is 1.

Let 100 be the nthnth term.

⟹100=51+(n−1)1⟹100=51+(n−1)1

⟹100=51+n−1⟹100=51+n−1

⟹100=50+n⟹100=50+n

⟹n=100−50⟹n=100−50

⟹n=50⟹n=50

100100 is the 50th50th term

There are 50 terms in this A.P.

The formula for finding sum of n terms in an A.P. is :

Sn=n2[2a+(n−1)d]Sn=n2[2a+(n−1)d] _____________________________________(1)

where,

SnSn - Sum of n terms of an Arithmetic Progression.

n - Number of terms .

a - First term of the Arithmetic Progression.

d - Common Difference.

Putting values from the question in (1)

⟹S50=502[2(51)+(50−1)1]⟹S50=502[2(51)+(50−1)1]

⟹S50=25102+50⟹S50=25102+50

⟹S50=25152⟹S50=25152

⟹S50=3800⟹S50=3800

Therefore, sum of all natural numbers from 51 - 100 is 3800.

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Answer 2

Answer:

The sum of all natural numbers from 61 to 100 is 3220

Step-by-step explanation:

Given two numbers are 61 and 100.

Sum of all natural numbers from 61 to 100 = (1+2+3+......+100) - ( 1+2+3+.....+60)

$= \frac{100 \times (100 + 1)}{2} - \frac{60 \times (60 + 1)}{2} \\ = (50 \times 101) - (30 \times 61) \\ = 5050 - 1830 \\ = 3220$

Therefore, required sum is 3220.

Know more about natural numbers:

The most primitive method of representing a natural number is to put a sign on each object. Later, a set of items can be tested for equality, excess, or deficiency by ticking down and removing the item from the set.

The first major advance in abstraction was the use of numbers to represent numbers. This made it possible to develop systems for storing large numbers. The ancient Egyptians developed a powerful number system with various hieroglyphs for 1, 10 and all powers from 10 to 1 million. A stone carving from Karnak, dating from about 1500 CE and now in the Louvre in Paris, represents 276 as 2 hundreds, 7 tens, and 6 ones; and likewise with the number 4622. The Babylonians had a place value system based primarily on the numbers 1 and 10, using sixties, so the sign for sixty was the same as the symbol for one - its value determined by context.

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