. Find the 100th term and the nth term for each of the sequences:
a) 8, 11, 14, 17, 20…
b) 1, 16, 81, 256, 625…
c) 5, 15, 45, 135, 405…
d) 2, 7, 12, 17, 22…
e) 1,1/2 1/4 1/8 1/16….

Hey I am not able to understand what it is …

I agree! But I think it was just supposed to be a carriage return.

dcarroll, these are quite straightforward.

Let's look at (a): the series starts at 8, and it increases by 3 every time after that. So we can write that series as x_n = 8 + 3(n-1), where n=1, 2, 3,.

How about (b): notice that each number is a perfect fourth power so we can write it as x_n = n^4.

Now (c): Notice that if you divide all the elements by 5 you get 1, 3, 9, 27, 81,. Those are all powers of 3 so we can write the series as x_n = 5\cdot 3^{n-1}.

I'll let you take care of (d) and (e). Note that (d) is quite similar to (a); each number differs from the previous one by a constant value. And (e) is another geometric series, meaning that it's a certain number raised to higher and higher exponents, like (c).

If you want to know the 100th term for any of those, just substitute 100 in place of n.

In fact, you only need to deduce whether the sequence is an arithmetic one or a geometric one.

An arithmetic one has general equation:

T_n = a + (n-1)d

Tn is the nth term, a is the first term and d is the common difference.

A geometric one has general equation:

T_n = ar^{n-1}

Tn is the nth term, a is the first term, r is the common ratio.