Question

Find sum of all natural number from 50 to 250 which are divisible by 6 and find Ap also.​

Answer 1

Answer:

Find the sum of all natural number between 50 and 250 which are divisible by 6

Answer: 4950.

Step-by-step explanation: These numbers will form an AP as follows:- 54,60,66,...,246 [common difference = 6] Here, a=54. aₓ=246 [last term] aₓ=a+(x-1)d. ...

∴x=33 terms. Sum of terms in AP, Sₓ = x/2 × (a+aₓ) = 33(246+54)/2.

minatiañ

Answer 2

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Using a formula for the sum of the first n natural numbers, i.e., n*(n+1)/2.

The sum of all numbers from 50 to 250 divisible by 6 can be written as:

6*(9 + 10 + 11 +… + 41) , since the range start with 54 and ends with is 246.

And the sum of all numbers from 1 to 250 divisible by 6 can be written as:

6*(1 + 2 + 3 + ….+ 41)

==> 6*(41*42)/2

==> 3 * 1722

==> 5166

The difference between the sum 6*(1 + 2 + 3 + ….+ 41)

and the sum 6*(9 + 10 + 11 +… + 41)

is 6 *(1 + 2 + 3 +… + 8)

==> 6 *(8*9)/2

==> 3 * 72

==> 216

Therefore the sum 6*(9+ 10 + 11 +… + 41) is

==> 5166 - 216

==> 4950.