An a.p has 17 terms and a common different of -4 determine the first and the last term of the a.p if it's sum is 107.1
Let the first term of the arithmetic progression be a, and the common difference be d.
The formula for the sum of an arithmetic progression is:
S = n/2(2a + (n-1)d)
where S is the sum of the AP, n is the number of terms, a is the first term, and d is the common difference.
Given that n = 17, d = -4, and S = 107.1, we can solve for a.
107.1 = 17/2(2a + 16(-4))
107.1 = 8.5(2a - 64)
107.1 = 17a - 544
17a = 651.1
a = 38.3
So, the first term of the AP is 38.3.
Now, we can find the last term by using the formula:
an = a + (n-1)d
an = 38.3 + (17-1)(-4)
an = 38.3 + 16(-4)
an = 38.3 - 64
an = -25.7
Therefore, the last term of the AP is -25.7.