In an arithmetic sequence the sum of the first 15 terms is 615 and the 13th term is six times the second. Find the first three terms.

Question

Geometric Progression

Answer 1

"the 13th term is six times the second" ---> a + 12d = 6(a+d)
a + 12d = 6a + 6d
6d = 5a
d = 5a/6
"the sum of the first 15 terms is 615"
---> (15/2)(2a + 14d) = 615
2a + 14d = 82
a + 7d = 41
use substitution:
a + 7(5a/6)= 41
6a + 35a = 246
41a = 246
a = 6 , then d = 5/6 (6) = 5

so you have 6 , 11, 16, ...

No idea what the "Geometric Progression" comment at the end of
your post is supposed to mean.