The sum, ${{S}_{n}}$, of the first $n$ terms of a sequence $\left\{ {{u}_{n}} \right\}$ is given by

Question

The sum, ${{S}_{n}}$, of the first $n$ terms of a sequence $\left\{ {{u}_{n}} \right\}$ is given by ${{S}_{n}}={{n}^{2}}-\left( k-2 \right)n$, where $k$ is a non-zero real constant. Prove that the sequence $\left\{ {{u}_{n}} \right\}$ is an arithmetic sequence. [3] Given that ${{u}_{8}},{{u}_{4}}$ and ${{u}_{2}}$ are the first $3$ terms in a geometric sequence, find the value of $k$. [2] Give a reason why the geometric series converges and find the value of sum to infinity. [2]

Accepted Answer

(ii) $k=1$, (iii) Since $\left| r \right|=\frac{1}{2}<1$ , the geometric series is convergent, ${{S}_{\infty }}=32$

2019 EJC Promo Q6

2019 EJC Promo Q6

Video Solution:

Solution:

Solution locked