Recurrence relations

The sum, $S_n$, of the first $n$ terms of a sequence $U_1,U_2,U_3,\ldots$ is given by

A sequence $u_1,u_2,u_3,\ldots$ is such that $u_1=\dfrac32$ and

(a) A sequence of real numbers $u_1,u_2,u_3,\ldots$ is such that

The $n$th term of a sequence is denoted by $a_n$. The sequence is defined by

A sequence $\{u_n\}$ is defined by

A sequence of real numbers $u_1,u_2,u_3,\ldots$ satisfies

The diagram shows $y=\ln(x-1)-x+4$. Its roots are $\alpha,\beta$, with $\alpha<\beta$.

A sequence of positive numbers satisfies

A sequence $u_1,u_2,u_3,\ldots$ is such that $u_1=1$ and

A sequence of real numbers $\{u_n\}$ satisfies

A sequence of positive real numbers satisfies

The diagram shows $y=\dfrac{x}{2^x}-\dfrac34x$. The two roots of $\dfrac{x}{2^x}-\dfrac34x=0$ are $0,\alpha$.

The diagram shows $y=x^5+2x-8$. Its root is denoted by $\alpha$.