sum of first 11 terms of AP is 44 and that of later 11 terms is 55 find the AP
Answers
Given : sum of first 11 terms of AP is 44 and that of later 11 terms is 55
To find : AP Series
Solution:
sum of first 11 terms of AP = 44
later 11 terms = 55
Sum of First 11 Terms
a + a + d + a + 2d +...........................................+ a + 10d = 44
Sum of Last 11 Terms
L + L -d + L - 2d +......................................... + L - 10d = 55
Adding all
=> 11a + 11L = 44 + 55
=> a + L = 9
=> L = 9 - a
Total terms = 11 + 11 = 22
L = a + (n-1)d
=> L = a + 21d
=> 9 - a = a + 21d
=> 21d = 9 - 2a
Sum of 1st 11 Terms
(11/2)(2a + 10d) = 44
=> 2a + 10d = 8
=> 2a = 8 - 10d
21d = 9 - ( 8 - 10d)
=> 21d = 1 + 10d
=> 11d = 1
=> d = 1/11
2a = 8 - 10d => a = 4 - 5d
=> a = 4 - 5/11
=> a = 39/11
AP Series
39/11 , 40/11 , 41/11 , ............................................ , 60/11
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