A few Math Problems Im stuck PLEASE HELP!!!!!!?

Question

here they are, please help with those you know. thank you soo much.

1. The sum of the first n terms of an arithmetic sequence {U sub n} is given by the formula S (sub n)= 4n^2 - 2n. Three terms of this sequence , U (sub 2) , U (sub m), U (sub 32), are consecutive terms in a geometric sequence. Find m.

2. The function f is defined for x > 2 by F(x)= ln (x) + ln (x - 2) - ln (x^2 - 4).
a) espress F(x) in the form ln [ x / (x +a) ].
b) find an expression for F^-1 (x).

please help with those you know. Thank you so much

Answer 1

Solution to Problem 1:
Let the first term of the arithmetic sequence to be A and the difference between two consecutive terms to be B. Hence the sequence is: A, A+B, A+2B, ..., A+(n-1)B, and the S(sub n) = nA + B(n^2 - n)/2 = 4n^2 -2n. Therefore, A = 2 and B = 8.
Also, U(sub 2) = 10, and U(sub 32) = A + 31B = 250.
U(sub m) = sqrt(2500) = 50 = A + 6B. Therefore m = 7

Solution to Problem 2:
a) F(x)= ln (x) + ln (x - 2) - ln (x^2 - 4)
= ln (x) + ln (x - 2) - [ ln (x-2) + ln (x+2) ]
= ln (x) - ln (x+2)
= ln [x/(x+2)]
b) I believe that you are looking for the inverse function, instead of 1/F(x). hence change x to F and F to x, we have:
x = ln [F/(F+2)], or
F/(F+2) = exp(x), or
F(x) = 2exp(x) / [1 - exp(x)]

Answer 2

not sure with reference to the 1st one as you ought to understand the cost carbon-14 degrades at. polynomial is (2x-3)(4x+3) 10x^2 +2 -[6(x^2-8)+7] = 10x^2 +2 -[6x^2 -40 8 +7] = 10x^2 +2 -6x^2 +40-one = 4x^2 + 40 3