Write an explicit formula for the following sequence. Find the tenth term.

Question

7​, 8​, 9​, 10​, 11​, ...
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Part 1
What is an explicit formula for the given​ sequence?
a Subscript nequals
  
enter your response here
​(Simplify your​ answer.)

Answer 1

The given sequence is \(7, 8, 9, 10, 11, \ldots\). This is an arithmetic sequence where the first term \(a_1 = 7\) and the common difference \(d = 1\).

The explicit formula for the \(n\)-th term of an arithmetic sequence is given by:

\[ a_n = a_1 + (n - 1) \cdot d \]

Substituting the values of \(a_1\) and \(d\):

\[ a_n = 7 + (n - 1) \cdot 1 \]

This simplifies to:

\[ a_n = 7 + (n - 1) = 7 + n - 1 = n + 6 \]

So, the explicit formula for the sequence is:

\[ a_n = n + 6 \]

To find the tenth term (\(a_{10}\)):

\[ a_{10} = 10 + 6 = 16 \]

Thus, the tenth term is 16.

Answer 2

simplify the answer

Answer 3

The explicit formula for the given sequence can be simplified as follows:

\[ a_n = n + 6 \]

This is already in a simple form.

Thus, the explicit formula for the sequence is:

\[ a_n = n + 6 \]

And the tenth term of the sequence, \(a_{10}\), is:

\[ a_{10} = 10 + 6 = 16 \]

There’s no further simplification possible for either the explicit formula or the value of the tenth term. The final answers are:

Explicit formula:

\[ a_n = n + 6 \]

Tenth term:

\[ a_{10} = 16 \]