Find the sum of the terms of the finite geometric sequence 1, -2, 4, -8, ...,-8192.
How do i find the sum?
Can't be that, since the sign of the last term determines the sign of the sum:
1
1-2 = -1
-1 + 4 = +3
3 - 8 = -5
-5 + 16 = +11
...
What did you get for n where An = -8192?
a1=1, r=-2.
calculate which term (n=?) for an=-8192.
then use the formula for the sum
I have sum of 2731 is correct?
To find the sum of the terms of a finite geometric sequence, you can use the formula:
Sum = a * (r^n - 1) / (r - 1),
where 'a' is the first term, 'r' is the common ratio, and 'n' is the number of terms.
In this case, we have the first term, a = 1, and the common ratio, r = -2.
To find the number of terms, we need to determine at what point the sequence reaches -8192.
We can observe that each term is obtained by multiplying the previous term by -2. So let's find the exponent 'n' when -2^n equals -8192.
-2^n = -8192
Dividing both sides by -2, we get:
2^n = 4096
Taking the logarithm of both sides (with base 2) will give us the exponent 'n'.
log2(2^n) = log2(4096)
n = log2(4096)
Using a calculator, we find that n = 12.
Now, we have all the required values: a = 1, r = -2, and n = 12.
Plugging these values into the formula for the sum of a geometric sequence:
Sum = 1 * (-2^12 - 1) / (-2 - 1)
Simplifying the equation:
Sum = 1 * (-4096 - 1) / (-3)
Sum = (-4097) / (-3)
Finally, the sum of the terms of the finite geometric sequence is:
Sum = 1365.67