How do you find $a_{1}$ $a_1$ for each geometric series $S_{n} = \frac{381}{64}$ $S_n=381/64$ , r=1/2, n=7?

Question

2338 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-25T01:00:47

$a_{1} = 3$ $a_1 = 3$

We use the formula $s_{n} = \frac{a (1 - r^{n})}{1 - r}$ $s_n = (a(1 - r^n))/(1 - r)$ to find the sum of the first n terms of a geometric series.

$\frac{381}{64} = \frac{a (1 - {(\frac{1}{2})}^{7})}{1 - \frac{1}{2}}$ $381/64= (a(1 - (1/2)^7))/(1 - 1/2)$

$\frac{381}{64} = \frac{a (1 - \frac{1}{128})}{\frac{1}{2}}$ $381/64 = (a(1 - 1/128))/(1/2)$

$\frac{381}{64} = \frac{\frac{127}{128} a}{\frac{1}{2}}$ $381/64 = (127/128a)/(1/2)$

$\frac{381}{64} = \frac{254}{128} a$ $381/64 = 254/128a$

$a = \frac{\frac{381}{64}}{\frac{254}{128}}$ $a = (381/64)/(254/128)$

$a = 3$ $a = 3$

Hopefully this helps!

How do you find a_1a1a_1 for each geometric series S_n=381/64Sn=38164S_n=381/64, r=1/2, n=7?