AP Calculus
posted by Watermelon .
The 9th term of an arithmetic progression is 4+5p and the sum of the four terms of the progression is 7p10, where p is a constant.
Given that common difference of the progression is 5, find the value of p.

a+8d = 4+5p
d = 5, so
a+40 = 4+5p
I assume you mean the sum of the *first* 4 terms is 7p10,so
4/2 (a + a+3d) = 7p10
2(2a+15) = 7p10
4a + 30 = 7p10
So, rearranging things a bit, we have
a  5p = 36
4a  7p = 40
13p = 104
p = 8
a = 4
so, the sequence is
4,9,14,19,24,29,34,39,44,49
9th term is 4+40 = 44
sum of 1st 4 terms is 46 = 5610