Sabrina is ordering a custom circular glass table for her dining room. the tables are ordered based on the area of the tabletop, and the diameter of every tabletop is a whole number. she wants a table with enough room for at least 6 people and wants each person to have at least 5 feet of table edge space, so that it is not too crowded.

the minimum tabletop diameter sabrina should order is
feet.

the minimum tabletop area of the table sabrina should order is
square feet.

answer: 414,377,008

step-by-step explanation:

just multiply it

, 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