Questions: What is the sixth term in the sequence given by (an=n^2+2 n) ? (a6=) Ex: 5

Transcript text: What is the sixth term in the sequence given by $a_{n}=n^{2}+2 n$ ? \[ a_{6}=\text { Ex: } 5 \]

Solution

Step 1: Identify the Formula for the Sequence

The sequence is given by the formula:

\[ a_{n} = n^{2} + 2n \]

Step 2: Substitute the Value of $ n $

To find the sixth term, substitute $ n = 6 $ into the formula:

\[ a_{6} = 6^{2} + 2 \times 6 \]

Step 3: Calculate the Expression

Calculate the expression:

\[ a_{6} = 36 + 12 = 48 \]

The sixth term in the sequence is $\boxed{48}$.

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