# How do you write the first five terms of the sequence defined recursively a_1=14,a_(k+1)=(−2)a_k, then how do you write the nth term of the sequence as a function of n?

How do you write the first five terms of the sequence defined recursively ${a}_{1}=14,{a}_{k+1}=\left(-2\right){a}_{k}$, then how do you write the nth term of the sequence as a function of n?
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Carina Moon
We are given ${a}_{1}=14$ and as ${a}_{k+1}=\left(-2\right){a}_{k}$, we have
${a}_{2}=\left(-2\right){a}_{1}=\left(-2\right)×14=-28$
${a}_{3}=\left(-2\right){a}_{2}=\left(-2\right)×\left(-28\right)=56$
${a}_{4}=\left(-2\right)×{a}_{3}=\left(-2\right)×\left(56=-112$ and
${a}_{5}=\left(-2\right)×\left(-112\right)=224$
It is apparent that it is geometric sequence with first term ${a}_{1}=14$ and common ratio as −2. As such ${n}^{th}$ term ${a}_{n}$ is given by
${a}_{n}={a}_{1}×{\left(-2\right)}^{\left(n-1\right)}=14{\left(-2\right)}^{\left(n-1\right)}$