In an arithmetic sequence the seventh term exceeds the fourth term by 15 determine the common difference
term(7) = a+6d
term(4) = a+3d
a+6d - (a+3d) = 15
a+6d-a-3d=15
3d=15
d = 5
Oh, I see what you're trying to do here. You want to solve this math problem in a fun way, don't you? Well, let me give it a shot!
Hmm, an arithmetic sequence, huh? Well, I bet these numbers have been attending a math comedy club regularly, because they love to follow a pattern! Now, let's get to the punchline!
The fourth term walks up to the seventh term and says, "Hey, I'm gonna be 15 numbers behind you, just to keep things interesting!" And the seventh term nods and replies, "Sure, buddy! Let's make it a fun sequence!"
So, the common difference between them, my friend, is 15! They're just adding a little laughter to the mix. Keep those numbers rolling and enjoy the arithmetic amusement!
To determine the common difference in an arithmetic sequence, we need to find the difference between consecutive terms.
Let's denote the first term as 'a', and the common difference as 'd'.
According to the given information:
The seventh term (a + 6d) exceeds the fourth term (a + 3d) by 15.
So, we can set up the equation:
a + 6d = (a + 3d) + 15
By simplifying the equation, we have:
a + 6d = a + 3d + 15
Subtracting 'a' from both sides of the equation:
6d = 3d + 15
Subtracting 3d from both sides:
3d = 15
Dividing both sides of the equation by 3:
d = 5
Hence, the common difference in the arithmetic sequence is 5.
To determine the common difference in an arithmetic sequence, you can subtract any two consecutive terms of the sequence to find the difference between them.
Let's denote the common difference as "d".
The formula for the nth term of an arithmetic sequence is:
An = A1 + (n - 1) * d
where An is the nth term, A1 is the first term, n is the position of the term, and d is the common difference.
We are given that the seventh term exceeds the fourth term by 15. So, we can write the following equation:
A7 - A4 = 15
Using the formula for the nth term, we can substitute the values:
(A1 + 6d) - (A1 + 3d) = 15
Simplifying the equation:
3d = 15
Now we can solve for d by dividing both sides of the equation by 3:
d = 15 / 3
d = 5
Therefore, the common difference in the arithmetic sequence is 5.