On the coordinate plane below, quadrilaterals TRAP and HELP are similar to each other.

Which of the following options best describes the relationship between the areas of the quadrilaterals?

1. Quadrilateral TRAP has an area that is half the area of quadrilateral HELP.

2. Quadrilateral TRAP has an area that is four times the area of quadrilateral HELP.

3. Quadrilateral TRAP has an area that is one-fourth the area of quadrilateral HELP.

4. Quadrilateral TRAP has an area that is twice the area of quadrilateral HELP.

i did it myself and i got 4.2 (b) hope its right

step-by-step explanation:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for