Sum of a geometric series

[loxxii]

Find the sum (s) of a geometric series for which A1=48, An=3, and r=-1/2

Now, the formula is s = A1/1-r, so 48/1.5 = 32 is what I get.

However, the choices are
– 99, 33, 99, or 15

Why does the formula not use An and should I chose 33 since it is the closest? I am lost.

[Enrique]

[ QUOTE ]
Find the sum (s) of a geometric series for which A1=48, An=3, and r=-1/2

Now, the formula is s = A1/1-r, so 48/1.5 = 32 is what I get.

However, the choices are
– 99, 33, 99, or 15

Why does the formula not use An and should I chose 33 since it is the closest? I am lost.

[/ QUOTE ]


48 + (-24) + 12 + (-6) + 3 = 33.

[Enrique]

[ QUOTE ]
Find the sum (s) of a geometric series for which A1=48, An=3, and r=-1/2

Now, the formula is s = A1/1-r, so 48/1.5 = 32 is what I get.


[/ QUOTE ]

The formula you site is true if you go to infinity, that is you keep summing terms till infinity
48 - 24 + 12 - 6 + 3 - 3/2 + 3/4 - 3/8 + 3/16 - ...

But the problem tells you An = 3, hence you stop the sum at 3. The formula is different in that case. Either way, to sum five terms, there's no need of a formula.

[loxxii]

Oh