How do I write an equation and determine the 8th term: 7, 7.5, 7.75, 7.875...?

Question

nottim · Answer

Dunno if this helps, but X/Y chart?

turingtest · Answer

we are adding 0.5,0.25.,0.125
so the next term should be 
7.875+(0.125/2)=7.9375

anonymous · Answer

yup... but what kind of sequence is it? geometric or using the recursion formula?

anonymous · Answer

or arithmetic?

turingtest · Answer

sorry for the typos...

anonymous · Answer

because i have to show my work on how I got the answer.

turingtest · Answer

umm... I forgot the definitions, but it's not geometric.
$$n_0=7$$$$n_1=7+(0.5)^1$$$$n_2=n_1+(0.5)^2$$in general$$n_i=n_{i-1}+(1/2)^i=7+1/2^1+1/2^2+...+1/2^{i-1}+1/2^i$$

anonymous · Answer

ohhh!! It's recursion formula? Is it like when t1 = x; tn-1 = tn+1 - tn... etc?

turingtest · Answer

You can write it recursively as I did at first, but the last formula I gave is not recursive
eighth term:$$n_7=7+1/2^1+1/2^2+1/2^3+1/2^4+1/2^5+1/2^6+1/2^7$$

anonymous · Answer

ohh..

turingtest · Answer

the last way I wrote the formula that is not recursive is $$n_i=n_0+1/2^1+1/2^2+...+1/2^{i-1}+1/2^i$$the recursive way is$$n_i=n_{i-1}+1/2^i$$(note the two are equivalent)

anonymous · Answer

yup. Oouu, okay! Thank you!!