Review question

# What can we say if $a, x_1, x_2, x_3, x_4, x_5, b$ are in arithmetic progression? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R6405

## Question

1. The seven numbers $a, x_1, x_2, x_3, x_4, x_5, b$ are in arithmetic progression. Express $x_2$ in terms of $a$ and $b$, and show that $x_1+x_3+x_5=\dfrac{3}{2}(a+b)$.

Given also that the numbers $a, x_2, b$ are in geometric progression, and that $b\neq a$, express $b$ in terms of $a$.

2. A geometric series has common ratio $r,$ where $|r|<1.$ The sum of the first $n$ terms of the series is $S_n$ and the sum to infinity is $S$. Express $r$ in terms of $S_n, S$ and $n,$ and prove that the sum of the first $2n$ terms of the series is $\dfrac{S_n(2S-S_n)}{S}$.