Please see the following problem below and answer the questions. Thank you for your help.

1. What is a geometric sequence? 0 It is the sequence such that each term is obtained from the preceding one by multiplying by a real constant. 0 it is the sequence such that each term is obtained from the preceding one by adding a constant. 0 it is any non-constant sequence of numbers. 0 None of the answer choices are correct 2. What is an arithmetic sequence? 0 it is the sequence such that each term is obtained from the preceding one by multiplying by a real constant. 0 it is the sequence such that each term is obtained from the preceding one by adding a constant. 0 it is any non-constant sequence of numbers. 0 None of the answer choices are correct. 3. What is a constant sequence? 0 arithmetic sequence. 0 geometric sequence. 0 sequence which all terms are equal. 0 None of the answer choices are correct 4. What is the common ratio in the given geometric sequence? 0 r=0.25 O r=0.5 O r=1 0 None of the answer choices are correct. 5. What is the n th term of the geometric sequence with the initial term a1=a and the common ratio equal r? O an = a t n xr O an = a - nxr Oan = ax rn- 1 O an = axr6. What kind of series is used to represent the movement of the snail? O constant series. 0 arithmetic series. 0 geometric series. 0 All of the answer choices are correct 7. How much did the snail travel after 11 days? O 0.001m O 1.999 m O 1.299m O 0.999m8. What is the total distance the snail has to climb to get out of the well? 9. The Question says: "Every day it goes back up half the distance it has left to go up. " What hint does this sentence tells us? 0 The snail has less than 1m to climb up. 0 The snail climbs up 1/2 m every day. Therefore the distance it climbs is in a Geometric Sequence. 0 The distance which the snail climbs every day is in a constant ratio with the distance the snail climbed the previous day. Therefore the distance it climbs is in a Geometric Sequence. 0 The distance which the snail climbs every day is half more than the distance the snail climbed the previous day. Therefore the distance it climbs is in a Geometric Sequence. 10. The distance travelled by the snail can be determined by the formula: O 2k - 1 Sk = 2k-1 2k - 1 O SK = 2k 2k O Sk = 2k-1 2k - 1 O Sk = K2-1Problem: A snail fell in a 2m well and wants to go back up. Every day it goes back up half the distance it has left to go up. After 11 days, how much does it have left to climb? Round your answer on three decimals. Solution: Recognize that the distance which the snail climbs every day are elements of a geometric sequence because each term is obtained from the preceding one by multiplying with a real constant. It is not an Arithmetic sequence which is the sequence where each term is obtained from the preceding one by adding a constant. It is denitely not a constant sequence because all terms are not equal. The distance which the snail climbs every day is in a constant ratio with the distance the snail climbed the previous day. We should nd an initial term and a constant ratio between successive terms. We have to nd The sum of the n terms of the geometric series To recall, the sequence (an)nN such that each term is obtained from the preceding one by multiplying by a real constant is a geometric sequence. That means that any geometric sequence has the form a, ar, arz, ar3, where the constant r is called the common ration. Note that r can be positive, negative or zero. The rst term a is called the initial term and often is denoted by a1. It is easy to conclude that the formula for the nth term of a geometric sequence is on = arr-"'1 A geometric series is a sum of a geometric sequence of numbers. So, the series '11 +a2+a3+...+an is a geometric series with common ration r if the ratios between consecutive terms are equal, i.e. $3 an = =___= :7- a1 02 anel The term alis the rst or initial term. That means that a nite geometrical series is the following sum a1+a1>