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

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

20×21=420

Step-by-step 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

15.5

step-by-step explanation:

5

∑

n = 1

substitute n = 1, 2, 3, 4, 5 and sum the terms

= + + + 2² + 2³

= 0.5 + 1 + 2 + 4 + 8

= 15.5