SOLUTION: If the 6th term of an AP IS 121,find the sum of the first 11 terms

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Question 1037860: If the 6th term of an AP IS 121,find the sum of the first 11 terms

Answer by ikleyn(52808) About Me  (Show Source):
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If the 6th term of an AP IS 121,find the sum of the first 11 terms
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We can write 

a%5B7%5D  = a%5B6%5D%2Bd,   a%5B5%5D = a%5B6%5D-d,

a%5B8%5D  = a%5B6%5D%2B2d,  a%5B4%5D = a%5B6%5D-2d,

a%5B9%5D  = a%5B6%5D%2B3d,  a%5B3%5D = a%5B6%5D-3d,

a%5B10%5D = a%5B6%5D%2B4d,  a%5B2%5D = a%5B6%5D-4d,

a%5B11%5D = a%5B6%5D%2B5d,  a%5B1%5D = a%5B6%5D-5d.


Then 

 = 10%2Aa%5B6%5D.

Add a%5B6%5D, and you will get that the sum of the first 11 terms is equal to 11a%5B6%5D.

Hence, this sum is 11*21 = 231.

Answer.  231.