# Math Help - Help : Find Number Of Terms Of Geometric Series

1. ## Help : Find Number Of Terms Of Geometric Series

Hello All ,

i want to solve this geometric series please :

Number of Terms = M
Terms Start From = 1
The Last Term (An) Is 0.5 = 31/16

Find The Number Of Terms "M"

Thanks Sooo Much

2. One thing that bothers me about this is you say "The Last Term (An) Is 0.5 = 31/16". Presumably you are aware the 0.5 is NOT equal to 21/16 so that cannot mean what you say. What did you mean by that? Is it possible that the first term is 1, the "common ratio" is 0.5 and the sum of the first M terms is 31/16?

If that is the case then you need to solve $\frac{1- 0.5^{M-1}}{1- 0.5}= 2(1- 0.5^{M-1})= 2- 0.5^M= 31/16.$ for M.

3. NOTE : i've added a picture in this replay so you know what i mean

what i mean in (An) = 0.5

is the last term of the series is "grade of last term is" 0.5 "i dont know how but i got it like this "

ya the sum is 31 / 16

and the first term is A1 which is unknown value