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Find the value of ${S_5}$ if \[{S_n} = 5{n^2} + 11n\].

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Last updated date: 24th Jul 2024
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Answer
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Hint: - Here we simply go through by putting the value of n equal to 5 as given in the question because it asked at the value n=5

Complete step-by-step answer:
Here the given equation is \[{S_n} = 5{n^2} + 11n\].
And now we have to find the value at n=5 because it asked for ${S_5}$.
So simply put n=5 in the equation we get,
\[
   \Rightarrow {S_5} = 5{(5)^2} + 11(5) \\
   \Rightarrow {S_5} = 5 \times 25 + 11 \times 5 \\
   \Rightarrow {S_5} = 125 + 55 \\
  \therefore {S_5} = 180 \\
 \]
Hence the value of ${S_5}$ is 180.
Note:- Whenever we find such a type of question the key concept for solving the question is just simply put the value of the variable that is given in the question to get the answer. Here this is the equation with variable n and then it asked for the value when n=5. So just put 5 at the place of n in the equation to get the answer.