Q. 47 - Calculus

Question

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

$-3,7,17,27,\dots$

Step-by-Step Solution

Answer

The required form is $\{-3+10k{\}}_{k=0}^{\infty }$.

Step 1. Given information.

The given series is $-3,7,17,27,\dots$

Step 2. Required form.

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

$$\begin{gathered} c=-3, \\ c+d=7 \\ -3+d=7 \\ d=7+3 \\ d=10 \end{gathered}$$

Therefore,

$\{c+dk{\}}_{k=0}^{\infty }\text{ can be written as }\{-3+10k{\}}_{k=0}^{\infty }.$