1.7.3 Sigma notation (A-level only)

A sequence $u_1, u_2, u_3, \dots\,$ is defined by

\begin{aligned}u_1 &= p \\u_n &= 2u_{n-1} - 3, \quad n \geq 2\end{aligned}

a.

Find an expression for $u_2\,$ in terms of $p$ .

[1]

b.

Show that $u_3 = 4p - 9$ .

[2]

c.

Find $∑r=14ur\sum_{r=1}^4 u_r$ in terms of $p$ .

[3]

A sequence $u_1, u_2, u_3, \dots\,$ is defined by

\begin{aligned}u_1 &= p \\u_n &= 2u_{n-1} - 3, \quad n \geq 2\end{aligned}

a.

Find an expression for $u_2\,$ in terms of $p$ .

[1]

b.

Show that $u_3 = 4p - 9$ .

[2]

c.

Find $∑r=14ur\sum_{r=1}^4 u_r$ in terms of $p$ .

[3]

1.7.3 Sigma notation (A-level only) Questions