Please give the answers and solutions for each.

Question

1.If the second term is 2 and the seventh term of a geometric sequence is 64, find the 12th term.

2. Which term if the geometric sequence 18,54,162,486,... is 3,188,646?

3. Determine the geometric mean of 8 and 288

4.Find x if the geometric mean of 6 and x is 3sqrt2

5. Find two geometric sequences where the first term is 1 and the fifth term is 256

6. Insert the indicated number of positive geometric means between each pair of numbers.
a. 2 and 31.25 [2]
b. 17 and 272 [3]
c.1/5 and 1/15625 [4]
*What does this mean [number] ?(the one in my abc's questions)

7.What is the sum of the first 10 terms of the geometric series 6+18+54+162+...?

8. What is the sum of each infinite geometric series if it exists ?
a.3-2+4/3-8/9+...
b. -1-0.1-0.01-0.001-...
c. sqrt2+2+sqrt8+4+...

9. A rubber ball rebounds 3/5 of the height from which it falls. If it is initially dropped from a height of 30 meters, what total vertical distance does it travel before coming to rest ?

*CHALLENGE
1. The Fibonacci sequence is defined recursively by a sub 1 = a sub 2 = 1 and a sub n+2 = a sub n+1 + a sub n for n > 1 . The first 5 terms of the said sequence is 1,1,2,3,5. what is the sum of the digits of the LCM of the first 10 terms of the Fibonacci sequence ?

2. In the triangular array of inters at the right, what the sum of the intergers in the 100th row ?
1
3 5
7 9 11
13 15 17 19
21 23 25 27 29
31 33 35 37 39 41

3. The sum of the first 4 terms of an arithmetic sequence a sub 1, a sub2 , a sub 3, a sub 4 is 2012 and the said 4 terms also form a geomeric sequence . Find a sub 4.

4. the 7th term of a geometric sequence is 20 and the 13th term is 12. Find the 10th term.

5. how many terms of the sequence -7,-4,-1,2,5,8,... must be taken to get a sum of 143?

6. the 5oth term of an arithmetic sequence exceeds the 10th term by 240. if the last digit of the 50th term is 8, what is the last digit of the 2012th term ?

7. the arithmetic mean of two positive integers is 1/2 more than their geomtric mean. if one of the integers is 1, what is the other integer ?

8.Find the sum of the first 2012 terms of the sequence 1+3-5+7+9-11+13+15-17+...

9.the sum of the arithmetic mean and the geometric mean of 2 positive numbers is 2012. what is the sum of the positive square roots of the 2 numbers ?

10. wat is the sum of 3 distinct positive integers whose geometric mean is 7 ?