+1124 Hi friends,
I have stumbled upon a problem which I believe is not solveable, am I doing something wrong or is it one of those sums?
Above the Sigma notation we have "m"
Bottom we have k=1
The expression is: (2)8−k=25512
Determine "m"
Okay, I calculated T1, and got 128
T2, and got 64
Since it is stated that this is an Arithmetic sequence, I know that d = -64
Using Sn=n2[2a+(n−1)d]
I get to a step where it says
64n2−320n+511=0
This is not solveable...I'm I doing something wrong here?..Please help. Thank you.
a=listfor(k, 1, 9, (2^(8 - k))
The above is your sequence. It is NOT arithmetic sequence but a GEOMETRIC sequence, where:
F==128 - this the first term, m ==9 - this is the number of terms, r ==1/2 - this is the common ratio.
So, your GS looks like this:
(128, 64, 32, 16, 8, 4, 2, 1, 0.5)==255.5 {As you can see here, r ==1/2}
You sum it up using the sum formula for GS:
{128 * [( 1 - 1/2^9) / (1 - 1/2)]}==S
{128 * [(1 - 0.001953125) / (1/2)]}==S
{128 * [0.998046875 / 0.5]} ==S
{128 * 1.99609375} ==255.5 - which is the answer you want.
+1124 Hi guest,
Thank you...yes the paper indicated this was an Arithmetic sequence...no wonder I got stuck...Thank you.
+118703 Hi Juriemagic,
m∑k=128−k=255.5
First I did a little spreadsheet to see if it worked
You can see that the answer is 9.
Now I will try it without the help of Excel.
The sequence is 128, 64, 32, 16 ,....
This is a GP with r=-0.5 and a=128
Sn=a(1−rn)1−rSn=128(1−(0.5)n)0.5=255.5 256(1−(0.5)n)=255.5 1−(0.5)n=255.5256 1−255.5256=(0.5)n 0.5256=12n 1512=12n 2n=512 n=9
+1124 Hello Melody,
mmm, I know I would have gotten it right if it was'nt for the misleading info that this was an Arithmetic sequence. Let this be a lesson to ALWAYS calculate the 3rd term as well and MAKE SURE the sequence is indeed what the paper says it is. Thank you very much Melody...I do appreciate..
