Question

question 22
find a formula for the general term ( a_n ) of the sequence assuming the pattern of the first few terms continues.
( {11, 12, 13, 14, 15, dots} )
assume the first term is ( a_1 ).
( a_n = )
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Explanation:

Step1: Identify sequence type

The sequence {11, 12, 13, 14, 15,...} is arithmetic. The first term \(a_1 = 11\), common difference \(d = 1\) (since \(12 - 11 = 1\), \(13 - 12 = 1\), etc.).

Step2: Use arithmetic sequence formula

The formula for the \(n\)-th term of an arithmetic sequence is \(a_n = a_1 + (n - 1)d\). Substitute \(a_1 = 11\) and \(d = 1\):
\(a_n = 11 + (n - 1)(1)\)
Simplify: \(a_n = 11 + n - 1 = n + 10\).

Answer:

\(a_n = n + 10\)