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Chapter 8: Problem 6

Write the first six terms of each arithmetic sequence. $$a_{1}=200, d=-60$$

Short Answer

Expert verified
The first six terms of the arithmetic sequence are 200, 140, 80, 20, -40, -100.

Step by step solution

01

Determine the First Term

The first term of an arithmetic sequence is always given directly, so in this case, \(a_{1}=200\).
02

Find the Second Term

The second term (\(a_{2}\)) can be found by adding the common difference to the first term. So, \(a_{2}=a_{1}+d=200+(-60)=140\).
03

Find the Third Term

Similarly, the third term (\(a_{3}\)) can be found by adding the common difference to the second term. So, \(a_{3}=a_{2}+d=140+(-60)=80\).
04

Find the Fourth Term

Continuing in the same way, the fourth term (\(a_{4}\)) can be found by adding the common difference to the third term. So, \(a_{4}=a_{3}+d=80+(-60)=20\).
05

Find the Fifth and Sixth Terms

Following the same pattern, the fifth term (\(a_{5}\)) and the sixth term (\(a_{6}\)) are obtained by adding the common difference to the fourth and fifth terms respectively. Therefore, \(a_{5}=a_{4}+d=20+(-60)=-40\) and \(a_{6}=a_{5}+d=-40+(-60)=-100\).

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