Complete the sequence of numbers in the set. Explain the pattern. The completed sequence of numbers is 8.5, 7.15, 5.8, blank and
blank. fill it in

Step-by-step explanation:

The first step to solve this question is to analyze the given sequence.

We can notice that the difference between 8.5 and 7.15 is

And again the difference between the second and the third term is :

One way to describe all the numbers in the sequence is by using a formula.

We can write :

Given the sequence

with ∈ I

For example :

  which verifies our original sequence.

We can obtain any term we want of the sequence.

Some of the terms that complete the sequence are :

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.