Question

Look at the table. Make a conjecture about the sum of the first 30 positive even numbers. The sum is 30 × 30. The sum is 31 × 32. The sum is 30 × 31. The sum is 29 × 30. mc007-1.jpg

Answer 1

the answer is 30*31

Explanation:

Answer 2

even numbers are represented by 2n
they are 2n, 2(n+1), 2(n+2) etc until 2(n+29)

we can do a summation of a seqeucne
the nth even number is an=2+2(n-1)

the sum of a sequence of n terms, where the first term is a1 and the last one is an is

`(n(a1+an))/(2)`

first term is 2
last one is 2+2(30-1)=2+2(29)=60


`(30(2+60))/(2)`=

`(30(62))/(2)`=
30*31
the answer is 30*31