Posted by Terfa sakaa on Sunday, October 14, 2012 at 4:28am.
I assume that "a,p" stands for arithmetic progression. Let the nth term be an.
Since a4 + a6 = 2 a5, a5 = 21.
Since a3 + a9 = 2 a6, a6 = 26
The common difference is
a(n+1) - an = a6 - a5 = 5.
The first term is 1, and the progression is
a1 = 1, a2 = 6, a3 = 11, a4 = 16,
a5 = 21, a6 = 26, a7 = 31, a8 = 36,
a9 = 41, a10 = 46...
The sum of the first 10 terms is
7 + 27 + 47 + 67 + 87 = 235