Question

Write each of the arithmetic sequences in Exercises 47–50 in the form $\{c+dk{\}}_{k=0}^{\infty }$

$5,\pi ,\dots$

Short answer

The required form is$\{5+(\pi -5)k{\}}_{k=0}^{\infty }$.

Step-by-step solution

Step 1. Given information.

The given series is$5,\mathrm{\pi }....$

Step 2. Comparison.

On comparing the given series to $\{c,c+d,c+2d,\dots \}$, we get,

$$\begin{gathered} c+d=\pi \\ d=\pi -5 \\ c=5 \end{gathered}$$

Step 3. Final answer.

Now,

$\{c+dk{\}}_{k=0}^{\infty }\text{can be written as}\{5+(\pi -5)k{\}}_{k=0}^{\infty }.$