Sequences and Series

In a geometric sequence $x1,x2,x3,…x_1, x_2, x_3, \dots$ :

a.

Show that $r\,$ satisfies the equation

3r^2 - 2r - 2 = 0

[4]

b.

Given that the geometric sequence has a sum to infinity,

find the exact value of $x_1\,$ in the form $b\sqrt{7}$ where $\in \mathbb{Q}$ .

[4]

c.

Hence, calculate the value of $S∞S_\infty$ .

[2]

In a geometric sequence $x1,x2,x3,…x_1, x_2, x_3, \dots$ :

a.

Show that $r\,$ satisfies the equation

3r^2 - 2r - 2 = 0

[4]

b.

Given that the geometric sequence has a sum to infinity,

find the exact value of $x_1\,$ in the form $b\sqrt{7}$ where $\in \mathbb{Q}$ .

[4]

c.

Hence, calculate the value of $S∞S_\infty$ .

[2]

Sequences and Series Questions