p+3; 2p - 3; p - 5
using arithmetic sequence how many terms of the sequence must be added to give a sum of -984
To find how many terms of the sequence must be added to give a sum of -984, we need to first find the formula for the arithmetic sequence.
The formula for the nth term of an arithmetic sequence is:
An = a + (n-1)d
where:
An = nth term
a = first term
n = number of terms
d = common difference
From the given terms, we have:
a = p + 3
2p - 3 = a + d
p - 5 = a - d
Let's solve for a, d, and p using the given information:
1. Solve for a:
a = p + 3
2. Solve for d:
a + d = 2p - 3
p + 3 + d = 2p - 3
d = 2p - 3 - p - 3
d = p - 6
3. Solve for p:
a - d = p - 5
p + 3 - p + 6 = p - 5
9 = -5
Since the equation resulted in a non-sensible answer, let's try to find p using a different method.
Given that the sum is -984, we can use the formula for the sum of an arithmetic sequence:
Sn = n/2(2a + (n-1)d)
Plugging in the values:
-984 = n/2(2(p + 3) + (n-1)(p-6))
This equation cannot be solved without knowing the value of p. We are unable to determine how many terms of the arithmetic sequence must be added to give a sum of -984 with the information provided.