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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 possible value of n such that the nth term is greater than 130.
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4 stepsHere's how to find the least possible value of .
Find the formula for the th term () of the AP.
The sum of the first terms is given by .
The th term, , can be found using the relationship .
First, find :Now, calculate :
Set up the inequality based on the given condition.
The problem states that the th term is greater than 130.
Substitute the expression for :
Solve the inequality for .
Add 9 to both sides of the inequality:
Divide by 2:
Determine the least possible integer value of .
Since must be an integer (as it represents the term number in a sequence) 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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