Question

If ${a}_{n} = \dfrac{n^2}{2^n}$ Find the value of $a_7$

Answer 1

Hint: Substituting the value of n directly into the general term will give us the answer.

Complete step-by-step answer:
Whenever we are given a formula for a general term in any question and we are required to get any specific term we then simply put the value of that specific term or in our case put the value of the variable of our general term $n$. In our question we have $n = 7$ and on putting this in our equation we get the value of $a_7^{}$
put $n = 7$
$a_7^{} = \dfrac{{7 \times 7}}{{{2^7}}}$
Now on putting the value of $n = 7$we get this and on simplifying this we get our answer as
$a_7^{} = \dfrac{{49}}{{128}}$
Hence the answer is $a_7^{} = \dfrac{{49}}{{128}}$

Note:While doing such questions we should always put the value of $n$ in the general term and get the answer and we should be careful while substituting the value of $n$.