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Is it true that if the sum of first ‘n’ natural numbers is given by $12 n 2 + 12 n$ , then the sum of natural numbers from 11 to 30 is 98?

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True

False

answer is B.

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Detailed Solution

Given data,
The sum of first n natural number =

12 n 2 + 12 n

.
We will subtract

S 11 f r o m S 30

to calculate the sum of natural numbers from 11 to 30.
Consider the expression

12 n 2 + 12 n

and putting

n = 30

to calculate sum of first 30 natural numbers,

S 30 = 12302 + 1230 = 9002 + 302 = 900 + 30 2 = 9302

S 30 = 465

The sum of first 11 natural number is 66,
We will now subtract

S 11 f r o m S 30

to calculate sum of natural numbers from 11 to 30,

S = S 30 − S 11 = 465 − 66 S = 399

Therefore, the sum of natural numbers between 11 and 30 is 399.
Hence, option 2 is correct.

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