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The sum of the first n terms of an arithmetic progression is given by S_n = n2 − 8n. Find the least integer n for which the nth term is greater than 130.
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Step-by-step solution
5 stepsFind the formula for the term, .
The sum of the first terms of an arithmetic progression is given by .
The term, , can be found using the relationship .First, find by substituting for in the formula for :
Calculate .
Now, substitute and into the formula for :
Set up the inequality.
The problem states that the term of the sequence is greater than 130:
Substitute the expression for :
Solve the inequality for .
Add 9 to both sides:
Divide by 2:
Determine the least possible integer value of .
Since must be an integer (as it represents the term number) and must be greater than 69.5, the least possible integer value for is 70.
The least possible value of is .
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