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

Suggestion

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 $a$.

Can we work out $d$, the common difference in the arithmetic progression?