How do I write an equation for: 7, 7.5, 7.75, 7.875, ...? Do I use the geometric sequence formula or recursion formula? Please help!

Question

anonymous · Answer

And be able to determine the 8th term?

kinggeorge · Answer

This looks like a geometric sequence to me$$7, 7+{1 \over 2}, 7+{1 \over 2} +{1 \over 4}, 7+{1 \over 2} +{1 \over 4}+{1 \over 8},...$$

anonymous · Answer

hmm..

kinggeorge · Answer

8th term would then be$$6+\sum_{i=0}^{7}{1 \over {2^i}}$$ I'm using 6 since the first term is 7, or 6+1

anonymous · Answer

what's the big E? o.O

anonymous · Answer

isn't the geometric formula: tn = a*r^n-1

kinggeorge · Answer

It's a summation symbol, just a different notation. In terms of the geometric formula, you're adding $${1}*{({1 \over 2})^{n-1}}$$ to 7 each time.

anonymous · Answer

ohhh.. i see.

anonymous · Answer

still kind of iffy about it..

kinggeorge · Answer

Since you're adding things, to get the actual n-th term, you would need to use the summation symbol I used previously. Basically, you increment the i from 0 to 7 and add up all the terms.

anonymous · Answer

ohhh :P okay!

kinggeorge · Answer

If you were looking for an explicit formula to get the 8th term, I don't know how to get it.