If the sum to infinity of the series `1 + 4x + 7x^2 + 10x^3 +.............` is `35/16` then `x=` (A) `1/5` (B) `2/5` (C) `3/7` (D)`1/7`

Explanation

To solve the problem, we need to find the value of \( x \) for which the sum to infinity of the series \( 1 + 4x + 7x^2 + 10x^3 + \ldots \) equals \( \frac{35}{16} \).

### Step-by-Step Solution:

1. **Identify the Series**:
The series can be expressed as:
\[
S = 1 + 4x + 7x^2 + 10x^3 + \ldots
...