Here are the first five terms of a sequence: 3/5, 3/4, 12/11, 12/7, 48/17, ... a) Find the general term. b) Determine if this sequence converges or diverges. If it converge, state the number

Question

can u help me with these questions by showing me the answer setp by step. I dont really understand.

Answer 1

Okay, let's see what we have: 3/5, 3/4, 12/11, 12/7, 48/17. Seemingly, a little confusing but it is not. Let's write it this way: starting from the second term multiply both numerator and denominator of every other term by 2. Then we get

3/5, 6/8, 12/11, 24/14, 48/17, ... . Now if you have a close look, you see how the next term can be obtained from the previous one; the numerator is doubling and denominator is adding by 3. So by this logic, the next term should be 96/20. Correct? Then we can write the general term as

a_n=(3*2^n-1)/(3n+2). I suppose you can figure out if it is convergent or not.

Any questions, feel free to ask.