+2666 The common ratio of the series is \(b \over 7\), and the starting term is \(b \over 7\), so we have the equation: \(\large{{{b \over 7} \over 1 - {b \over 7}} = 7}\)
Multiplying the entire equation by \(1 - {b \over 7}\) gives us \({b \over 7} = 7(1 - {b \over 7})\), which simplifies to \({b \over 7} = 7 - b\).
Multiplying the entire equation by 7 gives us \(b = 49 - 7b\), meaning \(b = \color{brown}\boxed{49 \over 8}\)
