What is the sum of the first five terms of the geometric sequence in which a1 = 10 and r = 1/2? Express your answer as an improper fraction.

Question

johnweldon1993 · Answer

The sum of the first 'n' terms can be given as..

$$\large a_n = a\frac{1 - r^{n}}{1 - r}$$

so for the first 5 terms here...with a = 10 and r = 1/2 we have...

$$\large a_5 = 10\frac{1 - \frac{1}{2}^{5}}{1 - \frac{1}{2}}$$

Can you solve this?

anonymous · Answer

well for 1-1/2^5 I got 9.6, would I multiply that part by 10? I'm confused @johnweldon1993

johnweldon1993 · Answer

Well 9.6875...hard to round that but I would just use this...

so yes multiply that by 10 to get 9.6875

so now you have...

$$\large S_5 = \frac{9.6875}{.5}$$

Right?

Now just evaluate that...*or actually your question states to leave your answer in an improper fraction...so this may be all you need to do...

anonymous · Answer

so I dont need to simplify that? the sum of the 5 numbers would simply be 9.6875/.5?

johnweldon1993 · Answer

If you want to simplify it go ahead...but based on what the question states...this would be the correct form...

if you want to evaluate it obviously it would be 19.375

anonymous · Answer

thank you :)

anonymous · Answer

it says that the correct answer was 155/8

johnweldon1993 · Answer

Yeah that is the correct answer....both in numerical form = 19.375

We just had the wrong fraction apparently..still correct though