THE 4TH TERM IS 37 AN THE 6TH TERM IS 12 MORE THAN THE 4TH TERM .FIND THE FIRST AN SEVENTH TERM
To find the first and seventh term, we need to determine the pattern or rule that the sequence follows. Let's break down the given information step by step.
We know that the fourth term is 37. Let's denote it as a variable:
Fourth term = x = 37
We are also told that the sixth term is 12 more than the fourth term. Let's denote the sixth term as a variable and use the value of the fourth term to find it:
Sixth term = x + 12 = 37 + 12 = 49
Now that we have the values for the fourth and sixth terms, we can find the pattern or rule that governs the sequence. We can do this by looking at the differences between consecutive terms:
Difference between consecutive terms:
2nd term - 1st term = x - (x - 3)
3rd term - 2nd term = (x - 3) - (x - 6)
4th term - 3rd term = (x - 6) - x
5th term - 4th term = x - (x + 3)
6th term - 5th term = (x + 3) - (x + 6)
From the differences, we can see that the common difference between consecutive terms is -3.
Now that we have the common difference, we can find the first term by working backward from the fourth term:
Fourth term = First term + 3 * (number of terms - 1)
37 = First term + 3 * (4 - 1)
37 = First term + 3 * 3
37 = First term + 9
First term = 37 - 9
First term = 28
Finally, we can find the seventh term by using the common difference and the first term:
Seventh term = First term + 3 * (number of terms - 1)
Seventh term = 28 + 3 * (7 - 1)
Seventh term = 28 + 3 * 6
Seventh term = 28 + 18
Seventh term = 46
Therefore, the first term is 28 and the seventh term is 46.
I will assume that this is an arithmetic sequence.
fourth term = a+3d
sixth term = a+5d
sixth term = fourth term + 12
a+5d = a+3d + 12
2d = 12
d = 6
fourth term = 37
a+3d = 37
a + 18 = 37
a = .....
so,
first term = a = ...
7th term = a + 6d = .....