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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 value of n for which the nth term is greater than 130.
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Step-by-step solution
4 stepsFind the formula for the term, , using the given sum .
The sum of the first terms of an A.P. is given by .
The term, , can be found using the formula .First, find by replacing with in the formula:
Expand the expression:
Now, substitute and into the formula for :
Set up the inequality based on the given condition.
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 (representing the term number), the least integer value of that is greater than 69.5 is 70.
The final answer is .
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