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Concept explainers
a.
To write a formula for the nth term of the given descriptions
a.
![Check Mark](/static/check-mark.png)
Answer to Problem 3.6.7P
The expression for the nth term for the given description is,
Explanation of Solution
Given information:
First term (a1) is negative
Common difference (d) is also negative
Formula Used:
Arithmetic sequence formula is,
Where, an is the nth term
a1 is the first term of the sequence
d is the common difference.
Calculation:
Let the first term (a1) be “-a ”
And the common difference (d) be “-d ”
Substituting the value in the arithmetic sequence formula,
Opening the brackets,
Conclusion:The expression for the nth term for the given description is,
b.
To write a formula for the nth term of the given descriptions
b.
![Check Mark](/static/check-mark.png)
Answer to Problem 3.6.7P
The formula for the nth term of the given descriptions is,
Explanation of Solution
Given information:Second term is -5
Common difference (d) is 7
Formula Used:
Arithmetic sequence formula is,
Where, an is the nth term
a1 is the first term of the sequence
d is the common difference.
Calculation:
For the first term, substituting the values in arithmetic sequence,
So,
Shifting left hand side values to right hand side,
On solving,
Hence, first term of the sequence is -12
For the formula of the nth term, substituting the values,
On re-arranging the variables,
Conclusion:The formula for the nth term of the given descriptions is,
c.
To write a formula for the nth term of the given descriptions
c.
![Check Mark](/static/check-mark.png)
Answer to Problem 3.6.7P
The formula for the nth term of the given descriptions is,
Explanation of Solution
Given information: Second term is 8
Third term is 6
Formula Used:
Arithmetic sequence formula is,
Where, an is the nth term
a1 is the first term of the sequence
d is the common difference.
Calculation:
For the common difference (d),
Subtracting third and second term,
On solving,
Hence, common difference is -2
For the first term, substituting the values in arithmetic sequence,
So,
Shifting left hand side values to right hand side,
On solving,
Hence, first term of the sequence is 10
For the formula of the nth term, substituting the values,
On solving,
Conclusion: The formula for the nth term of the given descriptions is,
Chapter ISG Solutions
Algebra 1, Homework Practice Workbook (MERRILL ALGEBRA 1)
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