That certainly seems like a doozy when you read it. But I think it can be handled.
From the tone of your question, and the fact that you appear to have solved
part a) and part b), I'm pretty sure that you have no trouble with a plain old
arithmetic sequence or a plain old geometric sequence. So let's look at the
numerator sequence and denominator sequence of c) separately.
Numerators: 1, 4, 7
Arithmetic sequence. General term = 3n - 2
Denominators: 5, 15, 45
Geometric sequence. General term = 5 x 3^(n-1)
(I always had trouble with these.
That one took me almost 15 minutes.)
So now ! Isn't the general term of the fraction sequence just
(3n - 2) / [ 5 x 3^(n-1) ] ?
and the 7th term would be
(3x7 - 2) / (5 x 3⁶) = (21 - 2) / (5 x 729) = 19 / 3,645
Definitely a weird number, but I feel like my approach holds water.
What do you think ?
