What is the 20th term in the sequence 1/2, 2, 7/2, 5

2-0.5=1.5
3.5-2=1.5
Therefore difference is 1.5=n
1.5n-1 is nth term
When n=20
=29

75

Step-by-step explanation:

Refer to attachment

As the first step extending the segment BC until intersection with AD.

Since ∠A + ∠B = 90° we get right triangle by extending CB

Naming the segments a, b, c, d as pictured

The are of (ABCD) is equal to sum of areas of two right triangles:

Area = 1/2c(a+b) + 1/2bd

Substitute d with a-c as a = c+d, then:

Area = 1/2(ac+bc) + 1/2b(a-c) = 1/2(ac + bc + ab - bc) = 1/2(ab + ac)Area = 1/2(ab+ac)

Applying Pythagorean to small triangle:

10² = b² + (a-c)²100 = b² + a² - 2ac + c²

Applying Pythagorean to bigger triangle:

20² = (a+b)² + c²400 = a² + 2ab + b² + c²

Subtracting equations we got:

400 - 100 = a² + 2ab + b² + c² - (b² + a² - 2ac + c²)300 = 2ab + 2ac

This gives us the 4 times of the area which is 1/2(ab + ac), so the area is

300/4 = 75