# Thread: find the specified value for r and n

1. ## find the specified value for r and n

can anybody here help me on this problem.... i've been trying to solve them with the use of the formula of geometric sequence and geometric series. but i could not make it to the answer.

Given: 1. S sub 5 = 31/4 ; r = 1/2 ; what is first term?

2. S sub n = 94.5 ; r = 1/2 ; a sub n = 3/2 ; what is n?

Thank you so much

2. 1. $\displaystyle \frac{31}{4} = \frac{a\left[1-\left(\frac{1}{2}\right)^5\right]}{1-\frac{1}{2}}$. Simplify and solve for $\displaystyle a$.

2. $\displaystyle 94.5 = \frac{\frac{3}{2}\left[1 - \left(\frac{1}{2}\right)^n\right]}{1 - \frac{1}{2}}$. Simplify and solve for $\displaystyle n$.

3. thank you Prove it. it is ok to put 3/2 which is the n value in the place of a sub 1 or first term?