Question

Suppose the sequence \(\left\\{a_{n}\right\\}\) is defined by the explicit formula \(a_{n}=1 / n,\) for \(n=1,2,3, \ldots .\) Write out the first five terms of the sequence.

Short answer

Question: Write down the first five terms of the sequence defined by the explicit formula \(a_n = \frac{1}{n}\), for \(n=1,2,3, \ldots\). Answer: The first five terms of the sequence are \(1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}\).

Step-by-step solution

Write down the formula for the sequence

The given formula for the sequence is \(a_n = \frac{1}{n}\). We will use this formula to find the first five terms of the sequence by substituting the values of \(n\) from 1 to 5.

Calculate the first term (n=1)

To find the first term of the sequence, substitute \(n=1\) into the formula: \(a_1 = \frac{1}{1} = 1\).

Calculate the second term (n=2)

To find the second term of the sequence, substitute \(n=2\) into the formula: \(a_2 = \frac{1}{2}\).

Calculate the third term (n=3)

To find the third term of the sequence, substitute \(n=3\) into the formula: \(a_3 = \frac{1}{3}\).

Calculate the fourth term (n=4)

To find the fourth term of the sequence, substitute \(n=4\) into the formula: \(a_4 = \frac{1}{4}\).

Calculate the fifth term (n=5)

To find the fifth term of the sequence, substitute \(n=5\) into the formula: \(a_5 = \frac{1}{5}\).

Write down the first five terms of the sequence

Using the calculated values, the first five terms of the sequence \(\{a_n\}\) are: \(1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}\).