12. which one of the following is a geometric sequence? a. −7, 10, 23, 36, . . b. 8, 4, 2, 1, 1/2, 1/4, . . c. 2, −3, 9/2, −18/4 d. 0, 1, 2, 3, . .

Step-by-step explanation:

A geometric sequence or geometric progression is a sequence where each term after the first one can be found by multiplying a certain factor.

So, basically, to find the geometric sequence, we just need to divide the second term by the first term and observe if it results a constant factor.

By doing that, we observe that the second equence is a geometric sequence with a reasonf of 1/2, let's demonstrate it

As you can observe, we perfectly built the sequence is its ratio or factor.

Therefore, choice B is a geometric sequence.

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.

the first one is x^2+2x+2

the second one is x^2+4

the last one is x^2-4x+8