Find a formula for the nth term of the sequence, assuming the pattern continues.

{2/3, 3/8, 4/13, 5/18, 6/23, 7/28, ...}

Find a formula for the nth term of the sequence, assuming the pattern continues.

{1/9, -4/27, 9/81, -16/243, -36/2187, ...}

Consider the following geometric series:

1/5 + 6/25 + 36/125 + 216/625 + 1296/3125 + 7776/15625 + ...

i) Find a formula for the nth term, assuming the pattern continues.

ii) Write the series in standard form and provide the values for a and r.

iii) Does the geometric series converge? If it does converge, find its sum.

Consider the following geometric series:

3 - 9/4 + 27/16 - 81/64 + 243/256 - 729/1024 + ...

i) Find a formula for the nth term, assuming the pattern continues.

ii) Write the series in standard form and provide the values for a and r.

iii) Does the geometric series converge? If it does converge, find its sum.