Identify the following series as arithmetic, geometric, both, or neither.
1/4 + 2/5 + 3/6 + 4/7
I know that the general term is n/n+3 but because the difference isn't something concrete, for example.. 4,6,8,10 d=2, would it be neither?

Question

Identify the following series as arithmetic, geometric, both, or neither.
1/4 + 2/5 + 3/6 + 4/7
I know that the general term is n/n+3 but because the difference isn't something concrete, for example.. 4,6,8,10 d=2, would it be neither?

shubhamsrg · Answer

nep..neither..

shubhamsrg · Answer

i meant yep**

anonymous · Answer

Okay, thank you!

jamesj · Answer

But do you know why it is neither?

jamesj · Answer

A series is arithmetic if and only if the difference of each pair of successive terms is equal.
You can see the difference 2/5 - 1/4 = 3/20 and 3/6 - 2/5 = 1/10 so the series isn't arithmetic.

Similarly, a series is geometric if and of only the ratio of each of pair of successive terms is equal.
$$ \frac{2/5}{1/4} = \frac{8}{5}$$
but
$$ \frac{3/6}{2/5} = \frac{5}{4} $$
Hence the series is not geometric either.

anonymous · Answer

Oh. That is very helpful! Thanks :) And for the geometric, what if it was like a sequence of 1,4,6,8. That wouldn't be geometric either because 1/4 is not equal to 3/4(6/8 reduced)?