Answer:
the 10th term is 75.
Explanation:
To find the first term, we can use the formula for the nth term of an arithmetic progression (A.P):
a + (n - 1)d = T
Where:
a is the first term,
n is the position of the term,
d is the common difference,
T is the value of the term at position n.
Given that the fifth term is 40 (T = 40) and the common difference is d:
a + (5 - 1)d = 40
a + 4d = 40
Also, given that the seventh term is 28 more than the third term:
a + (7 - 1)d = a + 6d = (a + 2d) + 28
So we have the following system of equations:
a + 4d = 40 ...(1)
a + 6d = (a + 2d) + 28 ...(2)
Simplifying equation (2):
a + 6d = a + 2d + 28
4d = 28
d = 7
Substituting the value of d into equation (1):
a + 4(7) = 40
a + 28 = 40
a = 40 - 28
a = 12
Therefore, the first term (a) is 12.
To find the 10th term, we can use the same formula:
a + (n - 1)d = T
Substituting n = 10, a = 12, and d = 7:
12 + (10 - 1)(7) = T
12 + 9(7) = T
12 + 63 = T
T = 75
Therefore, the 10th term is 75.