Sum of terms of an : where ' a ' is the first term and ' ' is the common difference.
n th term of an AP
Given Information:
(The sum of the first n terms is 700 ) (The 6th term is 7)
(The sum of the first 7 terms is 7 )
Steps to Solve:
Use to find a relationship between 'a' and 'd':

Use to find another relationship between ' a ' and ' d ':

Solve the system of equations (Equation 1 and Equation 2) to find ' ' and ' ':

Subtract Equation 1 from Equation 2:

Substitute into Equation 1:

Find ' n ' using :

Solve the quadratic equation for ' ':
We can use the quadratic formula:

We have two possible values for n:

be a positive integer, we discard this solution)

So,
Find (which is ):

Therefore, .

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