Form an arithmetic sequence by finding p in the numbers 7p+2, 5p+12, 2p-1...
What is the difference of the arithmetic sequence 7p+2, 5p+12, 2p-1?
come on, man!
The common difference is A2-A1 or A3-A2, which they gave you.
The difference is shown above:
-2p+10 or -3p-13
In either case, it is 56.
Now do you think you can write the sequence?
159,103,47,
I do not understand
find p so that p+5,2p+1,4p-1,... form an arithmetic sequence
To form an arithmetic sequence, we need to find a common difference between consecutive terms. In this case, we have the following numbers: 7p+2, 5p+12, 2p-1.
To find the common difference, we need to subtract each term from the next consecutive term.
The common difference (d) between the first and second terms is:
(5p+12) - (7p+2)
= 5p + 12 - 7p - 2
= -2p + 10
= -2(p - 5)
The common difference (d) between the second and third terms is:
(2p - 1) - (5p + 12)
= 2p - 1 - 5p - 12
= -3p - 13
For an arithmetic sequence, the common difference (d) remains constant for all terms. Therefore, we equate the common differences we found:
-2(p - 5) = -3p - 13
Let's solve this equation to find the value of p:
-2p + 10 = -3p - 13
To isolate the variables on one side, we can add 3p to both sides:
p + 10 = -13
Next, subtract 10 from both sides:
p = -13 - 10
p = -23
So, the value of p in the given sequence is -23.
since the difference is constant,
(5p+12) - (7p+2) = (2p-1) - (5p+12)
-2p+10 = -3p-13
p = -23
Now you can find the difference, and write the terms of the sequence.