Mathematics: In an arithmetic sequence, [tex] a_{17} [/tex] = -40 and [tex] a_{28} [/tex] = -73. explain how to use this information to write a recursive formula for this sequence.

In an arithmetic sequence, [tex] a_{17} [/tex] =

SkyeShadow525

12.03.2022

The common difference is equal the difference between the given terms divide by the difference between the term numbers:

$d=\dfrac{a_{28}-a_{17}}{28-17}\to d=\dfrac{-73-(-40)}{11}=\dfrac{-33}{11}=-3$

Calculate the first term:

$a_1=a_{17}-16d\\\\a_1=-40-16(-3)=-40+48=8$

The recursive formula is:

$a_n=\left\{\begin{array}{ccc}a_1=8\\a_{n+1}=a_n-3\end{array}\right$

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hmj192905

29.10.2020

6326169565453505

Step-by-step explanation:

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