Question

what conjecture can you make about the sum of the first 10 positive even numbers? . . 2 =2 = 1 x 2. 2 + 4 = 6 = 2x3. 2+4+6 = 12 = 3x4. 2+4+6+8 = 20 = 4x5. 2+4+6+8+10 = 30= 5x6. . . A] The sum is 9x10. B] The sum is 10x10. C] The sum is 11x12. D] The sum is 10x11

Answer 1

The correct option is D. The sum first 10 even numbers is 10x11.

Explanation:

The first even number is 2 and the sum of first even term is 2. The product form of the sum is

`1* 2`

The first two even number are 2,4 and the sum of first two even terms is 6. The product form of the sum is

`2* 3`

The first three even number are 2,4,6 and the sum of first three even terms is 12. The product form of the sum is

`3* 4`

The product form of the sum of ever term follows pattern. It is the product of n and (n+1), where n is the first n even numbers.

`n* (n+1)`

The pattern can be derived.

The sum of first n even numbers is

`S_n=2+4+6+8+---+2n`

`S_n=2(1+2+3+4+---+n)`

`S_n=2((n)/(2))(2(1)+(n-1)1)`

`S_n=n(2+n-1)`

`S_n=n(n+1)`

Therefore the sum of first 10 even numbers is

`S_(10)=10* (10+1)`

`S_(10)=10* (11)`

Therefore option D is correct.

Answer 2

sum of the first 10 positive even numbers can be represented as

2+4+6+8+...+20
=2(1+2+3+4+..+10)
=2*(1+10)*10/2=110

so the right answer is D The sum is 10x11