The first three terms of a sequence are given by ${{u}_{1}}=10$, ${{u}_{2}}=6$, ${{u}_{3}}=5$. Given

Question

The first three terms of a sequence are given by ${{u}_{1}}=10$, ${{u}_{2}}=6$, ${{u}_{3}}=5$. Given that ${{u}_{n}}$ is a quadratic polynomial in $n$, find ${{u}_{n}}$ in terms of $n$. [4] Find the set of values of $n$ for which ${{u}_{n}}$ is greater than $100$. [2]

Accepted Answer

(i) $u_n = \dfrac{3}{2}n^2 - \dfrac{17}{2}n + 17$ (ii) $\{n \in \mathbb{Z}^+ : n \geq 11\}$

N2009 P1 Q1

N2009 P1 Q1

Video Solution:

Default solution