Question

PLS HELP!!!
Look at the table. Make a conjecture about the sum of the first 10 positive even numbers.

https://dlap.gradpoint.com/Resz/~yUA6AAAAAAgWxQgHSmEpfA.WDcut6JqmpTx2pr6qYNrLA/7234256,15F/Assets/questions/test/geometry/geopatt/mc008-1.jpg

Answer 1

@Vocaloid

Answer 2

notice any interesting patterns from the table?

for every sum of (n) even numbers, the sum is given as (n)(n+1)

try to apply this logic to find the sum of the first 10 even numbers

Answer 3

(2)(2+1)=6
(6)(6+1)=42
(12)(12+1)=156
(20)(20+1)=420
(30)(30+1)=930

Answer 4

n is the number of terms, not the sum

notice how 2 + 4 + 6 has three terms, so n = 3 and the sum is (n)(n+1) = 3*4 = 12

try to apply this logic for n = 10 terms

Answer 5

(1)(1+1)=2
(2)(2+1)=6
3(3+1)=12
4(4+1)=20
5(5+1)=30

Answer 6

good but we need to extend this logic to n = 10

if n = 10 then (n)(n+1) = ?

Answer 7

10(10+1)=110

Answer 8

@Vocaloid

Answer 9

good so we would conjecture that the sum of the first 10 positive even #'s is 110