Question

Look at the table. Make a conjecture about the sum of the first 20 positive even numbers.

Answer 1

It will be 20*21 based on the pattern in the chart

Answer 2

Hence, the conjecture for the sum of first 20 positive integer is:

20×21=420

Explanation:

The table is given as:

2 = 2 =1.2

2+4 = 6 = 2.3

2+4+6 = 12 = 3.4

2+4+6+8 = 20 = 4.5

2+4+6+8+10 = 30 = 5.6

Hence, we see the pattern as:

2+4+6+....+2n= n(n+1)

which is the sum of first n even positive integers.

Hence, we are asked to find the sum of first 20 positive even numbers that is we are asked to find the sum when n=20.

i.e. the sum of:

2+4+6+8+..........+40=20(20+1)

2+4+6+8+........+40=20×21=420.

Hence, the conjecture for the sum of first 20 positive integer is:

20×21=420