[dcarroll2]

. 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….

[ApoorvGoel]

Hey I am not able to understand what it is …

[jcaron2]

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

[jcaron2]

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 , where n=1, 2, 3,.

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

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 .

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.

[Unknown008]

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

An arithmetic one has general equation:



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

A geometric one has general equation:



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