Given the geometric sequence that begins with the terms 2,1,... What is the sum of the first 12 terms?

The general term of a geometric series is arn−1, where r is the ratio, and a is the first term. In your case, a=2–√ and r=3–√. The 12th term is then

2–√(3–√)11=2436–√

The sum of the first 12 terms is

a∑k=011rk=ar12−1r−1=2–√7283–√−1=364(2–√+6–√)

Note that I used 35=243 and 36=729 in the above.

EDIT

Note that

2–√7283–√−1=2–√7283–√−13–√+13–√+1=2–√(3–√+1)728(3–√)2−12=(6–√+2–√)7283−1

Step-by-step explanation:

what do you need me to answer?

step-by-step explanation:

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.