Final answer:
The first term of the arithmetic progression is 90 and the common difference is -3.
Step-by-step explanation:
We can solve this problem by setting up a system of equations. Let's denote the first term as 'a' and the common difference as 'd'.
From the information given, we have:
a + 6d = 72 (equation 1)
2nd term = 7 * 5th term
a + 2d = 7(a + 4d)
a + 2d = 7a + 28d
6d - 26d = 7a - a
-20d = 6a
-10d = 3a
So we have two equations:
1) a + 6d = 72
2) -10d = 3a
We can solve this system of equations by substitution or elimination to find the values of 'a' and 'd'.
Let's use elimination method:
Multiply equation 1 by 3 and equation 2 by 6 to eliminate variable 'a':
3(a + 6d) = 3(72)
-60d = 18a
Combining the equations:
-60d = 18a
-10d = 3a
-60d = -20d
d = -3
Substitute the value of 'd' into either equation to find 'a':
a + 6(-3) = 72
a - 18 = 72
a = 90
So the first term is 90 and the common difference is -3.