Math, asked by akshara88017, 11 months ago

sum of first 11 terms of AP is 44 and that of later 11 terms is 55 find the AP​

Answers

Answered by amitnrw
2

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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