5; 1; -3
using arithmetic sequence how many terms of the sequence must be added to give a sum of -984
Let the first term be 5 and the common difference be -2 (since the sequence is decreasing by 2 each time).
The formula for the sum of an arithmetic series is: Sn = n/2 * (2a + (n-1)d),
where:
- Sn is the sum of the first n terms;
- a is the first term of the sequence;
- d is the common difference between the terms;
- n is the number of terms to be added.
In this case, we need to find how many terms must be added to give a sum of -984. So, we have:
-984 = n/2 * (2*5 + (n-1)(-2))
-984 = n/2 * (10 - 2n + 2)
-984 = n/2 * (-2n + 12)
-984 = -n^2 + 6n
n^2 - 6n - 984 = 0
Now, we solve for n:
n^2 - 6n - 984 = 0
(n - 36)(n + 30) = 0
n = 36 or n = -30 (n must be positive, so n = 36)
Therefore, 36 terms of the sequence must be added to give a sum of -984.