4 Find the area of the shape.
Either enter an exact answer in terms of T or use 3.14 for it and enter your answer as a decimal.

The answer is 37.68

We need to find the area of the sector of the circle.

There is a missing part in the upper left part of the circle.

The upper left part central angle measure 90 degree becuase it has a perpendicular sign.

Using central angle and arc theorem, the central angle equal the arc measure so that arc measure is 90 degrees.

There is 360 degrees in a circle so using arc addition,

the rest of the arc measure 270 degrees.

We can use this formula to find the area of the sector

where x is the measure of the central angle and r is the radius.

Plug 270 in for x. The radius is 4.

which is about

37.68

, 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