There are a couple of problems that I would need help on. Please show all work.
1) Find an explicit formula for the arithmetic sequence A5=10 and A8=2, and then use it to find the 12th term of the sequence.
2) Find three arithmetic means between 64 and 82.
3) Find the mean proportional between -8 and -14.
4) Find the partial sum S9 of: 2.2, 7.4, 12.6,...............43.8
5) Use the binomial theorem to expand and simplify (3a-2b^-1)^5
6) Find the ninth term of the expansion of (x-3y)^14
7) Use the principle of mathematical induction to prove that for all positive integers n, 1+3+5+.......+ (2n-1)=n^2
1) Find an explicit formula for the arithmetic sequence A5=10 and A8=2, and then use it to find the 12th term of the sequence.
2) Find three arithmetic means between 64 and 82.
3) Find the mean proportional between -8 and -14.
4) Find the partial sum S9 of: 2.2, 7.4, 12.6,...............43.8
5) Use the binomial theorem to expand and simplify (3a-2b^-1)^5
6) Find the ninth term of the expansion of (x-3y)^14
7) Use the principle of mathematical induction to prove that for all positive integers n, 1+3+5+.......+ (2n-1)=n^2