find p so that the numbers 7p+2, 5p+12, 2p-1...... form an arithmetic sequence
to be an AS,
5p+12 - (7p+2) = 2p-1 - (5p+12)
solve for p
-23
To find the value of p that makes the numbers 7p+2, 5p+12, and 2p-1 form an arithmetic sequence, we need to ensure that the difference between any two consecutive terms is constant.
Let's start by finding the difference between the second term (5p+12) and the first term (7p+2):
(5p+12) - (7p+2) = 5p+12 - 7p-2 = -2p+10
Next, let's find the difference between the third term (2p-1) and the second term (5p+12):
(2p-1) - (5p+12) = 2p-1 - 5p-12 = -3p-13
Since these two differences must be equal to form an arithmetic sequence, we can set them equal to each other and solve for p:
-2p+10 = -3p-13
To solve for p, we will isolate the variable on one side:
2p - 3p = -13 - 10
Simplifying the equation:
-p = -23
To solve for p, we need to multiply both sides of the equation by -1:
p = 23
Therefore, the value of p that makes the numbers 7p+2, 5p+12, and 2p-1 form an arithmetic sequence is p = 23.
To find the value of p that would make the numbers 7p+2, 5p+12, and 2p-1 form an arithmetic sequence, we need to determine if the difference between the consecutive terms is constant.
The common difference in an arithmetic sequence is the value we add or subtract to each previous term to obtain the next term. Let's calculate the difference between the second and first terms (5p+12) - (7p+2):
(5p + 12) - (7p + 2) = 5p + 12 - 7p - 2 = -2p + 10
Now, let's calculate the difference between the third and second terms (2p-1) - (5p+12):
(2p - 1) - (5p + 12) = 2p - 1 - 5p - 12 = -3p - 13
For the given numbers to form an arithmetic sequence, both differences should be equal. Therefore, we need to equate them:
-2p + 10 = -3p - 13
Let's solve this equation to find the value of p:
Add 3p to both sides:
-2p + 3p + 10 = -3p + 3p - 13
p + 10 = -13
Subtract 10 from both sides:
p + 10 - 10 = -13 - 10
p = -23
Therefore, the value of p that will make the numbers 7p+2, 5p+12, and 2p-1 form an arithmetic sequence is p = -23.