Question

The 9th term of an arithmetic progression is 4+5p and the sum of the four terms of the progression is 7p-10, where p is a constant.
Given that common difference of the progression is 5, find the value of p.

Answer 1

a+8d = 4+5p
d = 5, so

a+40 = 4+5p

I assume you mean the sum of the *first* 4 terms is 7p-10,so

4/2 (a + a+3d) = 7p-10
2(2a+15) = 7p-10
4a + 30 = 7p-10

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 = 56-10