Consider a geometric progression, where a1 represents the first term, and an represents the nth term. Each term of the progression is defined by the product of the previous term and the common ratio, r. The derivation of the formula for the finite sum of a geometric progression, where r < 1, is shown below, with a mistake at a key step. Steps Derivation Reasons 1 Given 2 Substitution 3 Multiply both sides by r 4 Subtracting Sr from S 5 Factor common terms 6 Division Determine the step where the first mistake occurs.

step-by-step explanation:

12

step-by-step explanation:

a triangle's   full angle is 180 degrees so 180 - 156 = 24. 24/2=12

50-60=10

step-by-step explanation:

a.) list the factors of 40.

1/2/4/5/8/10/20/40

b.) list the factors of 40 that represent the number of cans that could be on each shelf.

5

c.) how many different arrangements of cans are possible?

just one because if you put more on one shelf you will go way over 40 and the cabinet will probably break.

d.) what are the possible arrangements of the cans?

put 5 cans on each self to reach 40 cans in total.

e.) which arrangement uses all the shelves?

5 because you can put 5 cans on each shelf, and since there are 8 shelfs you are equally going to get 40 cans.