Gerard Sayson TMUA Mock Paper 1 · Question 13

Two geometric sequences $(u_n)$ and $(v_n)$ have the same first term $a$ , where $a\ne0$ . One sequence has a common ratio of $r$ and the other has a common ratio of $r^2$ , where $|r|<1$ .

The sum to infinity of $(u_n)$ is twice the sum to infinity of $(v_n)$ .

A new sequence is defined by $w_n=u_n^2$ for all $n\ge1$ . What is the sum to infinity of $(w_n)$ in terms of $a$ ?

\frac{4a^2}{3}

\frac{16a^2}{15}

\frac{16a^2}{9}

\frac{4a^2}{5}

\frac{8a^2}{3}

examday

Gerard Sayson TMUA Mock Paper 1 · Q13