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Given the sum of the first n terms of an arithmetic progression (A.P.) is S_n = n2 − 8n.
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6 stepsFind the formula for the sum, .
Given the sum of the first terms of an arithmetic progression (A.P.) is .
To find , substitute for :Expand and simplify .
Expand the expression:
Find the formula for the term, .
The term of an A.P. can be found using the formula .
Substitute the expressions for and :Set up the inequality based on the problem statement.
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 represents the term number, it must be an integer. The least integer value of that is greater than 69.5 is 70.
The least possible value of is .
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