Question

Answer in 10 Min.

What Is The sum of the first 30 Natural Number ?
1) 464
2) 465
3) 462
4) 461



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Answer 1

OPTION 2 - 465

Hint:

Natural numbers can be defined as the numbers which begin with the number one. Natural numbers are expressed as 1,2,3,4, ..... difference between any two consecutive terms is always one and therefore since there is a common difference between the terms, here we will use arithmetic progression.

Complete step by step answer:

Given that to find the Sum of 1st301st30 natural numbers.

Given that to find the Sum of 1st301st30 natural numbers.The above word statement can be expressed as – 1 + 2 + 3+ .... + 30

first term is a= 1

Common difference is d = 3−2 = 1

Also, here we have total number of terms, n=30

Sum of terms in the arithmetic progression can be given by –

$\\ \\ sn = \frac{n}{2} (a + l) \\ \ \\ \ = > s30 = \frac{30}{2} (1 + 30) \\ \\ \\ = > s30 = 15 \times 31 \\ \\ \\ = 465 \: \: \\ \\ \\ answer$

Note:

Always remember and know the concepts very clearly for the natural numbers, whole numbers, integers, natural numbers, prime numbers, the composite numbers, Rational and irrational numbers. Also, know the difference and co-relation between them. Also, remember the difference between the sequences and patterns of the series. When there is a common ratio between the terms then the series in the form of geometric progression and when there is a common difference between the consecutive terms then the series in the form of the arithmetic progression.

Answer 2

$\dag\rm \: \purple {To \: Find :-}$

• The sum of first 30 Natural Numbers

$\dag\rm \red { \: Given :-}$

The 1st 30 Natural Numbers are 1,2,3..30.

Then, the sum of them can be written as

=> 1 + 2 + 3..+ 30

Common difference (d) = 2 - 1 = 1

Total number of terms (n) = 30

$\dag \rm \blue { \: Solution :-}$

Sum of terms using arithmetic progression can be given as,

$\sf \leadsto \orange{ s = \frac{n}{2} (l + a)}$

Where,

• s = sum of terms
• n = number of terms
• a = first term
• l = last term

Therefore, putting the values, we get,

$\sf \leadsto \: s = \frac{30}{2} (1 + 30) \\ \sf \leadsto \: s = 15 \times 31 \: \: \: \: \: \: \: \\ \sf \leadsto \: s = 465 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\dag\rm \: \red{Note:-}$

• What is arithmetic progression?
• Arithmetic progression is a sequence of number in which the consecutive numbers are the resultant of addiction or subtraction of a particular number.
• How to calculate "common difference"?

${ \boxed { \sf \pink{ \star \: {common \: difference =second \: term - first \: term}}}}$