The 5th term of an arithmetic sequence is 20 and its 10th term is 35. The first term of a geometric sequence is the same as the first term of this arithmetic sequence, while the 4th term of the…

The 5th term of an arithmetic sequence is 20 and its 10th term is 35. The first term of a geometric sequence is the same as the first term of this arithmetic sequence, while the 4th term of the geometric sequence is 1. What will be the sum to infinity of the arithmetic-geometric sequence whose $n$-th term is given by $[a+(n-1)d]\times r^{n-1}$, where $a$ is the first term of both the arithmetic and the geometric sequences, $d$ is the common difference of the arithmetic sequence, and $r$ is the common ratio of the geometric sequence?