Determine an Ap whose 3rd term is 9 and fifth term when subtracted from 9th term we get 6
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padmalatha94:
8 term can be represented as a+7d but not with a+8d so the total sum is wrong
Sorry I posted wrong question
Actually it is 8th term but not 9th term what I need and I am so sorry deeprwt786 for posting the negative comment
its okk..@padamalatha94
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GIVEN :
IN AN AP :
=> 3RD TERM :
=> 9
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CONCEPTS NECESSARY TO ANALYSE AP :
=> A = T 1 = FIRST TERM IN ARITHMETIC PROGRESSION
=> T 2 = SECOND TERM
=> D = COMMON DIFFERENCE BETWEEN ANY 2 CONSECUTIVE TERMS
=> N = NO. OF TERM
=> S = SUM
=> SN = SUM OF N TERMS
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=> WE HAVE GIVEN THE THIRD TERM
STEP 1 :
=> USE FORMULA OF NO. OF TERM TO OBTAIN AN EQUATION
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FORMULA :
=> T N = A + D ( N - 1 )
=> T 3 = A + D ( 3 - 1 )
=> 9 = A + 2D
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CONDITION :
=> WHEN 5TH TERM IS SUBSTRACTED FROM 9TH TERM WE GET 6
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STEP 2 :
=> FIND 5TH TERM AND 9TH TERM BY FORMULA OF TN
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TN = A + D ( N - 1 )
=> T5 = A + D ( 5 - 1 )
=> T 5 = A + 4D
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T9 = A + D ( 9 - 1 )
=> T 9 = A + 8D
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FROM THE THE CONDITION :
=> T 9 - T 5 = 6
=> A + 8D - ( A + 4D ) = 6
=> A + 8D - A - 4D = 6
=> 4D = 6
=> D = 6 / 4
=> D = 3 / 2
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PUT D = 3 / 2 IN ANY EQUATION ,
=> A + 2D = 9
=> A + 2 * 3 / 2 = 9
=> A + 3 = 9
=> A = 9 - 3
=> A = 6
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T 2
=> A + D
=> 6 + 3 / 2
=> 12 / 2 + 3 / 2
=> 15 / 2
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T3
=> A + 2D
=> 6 + 2 * 3 / 2
=> 6 + 3
=> 9
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T4
=> A + 3D
=> 6 + 3 * 3 / 2
=> 6 + 9 / 2
=> 12 / 2 + 9 / 2
=> 21 / 2
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REQUIRED AP :
=> 6 , 15/2 , 9 , 21 / 2 , ........
______________________________
HOPE IT WILL HELP U ....
THANKS .....
______________________________
GIVEN :
IN AN AP :
=> 3RD TERM :
=> 9
______________________________
CONCEPTS NECESSARY TO ANALYSE AP :
=> A = T 1 = FIRST TERM IN ARITHMETIC PROGRESSION
=> T 2 = SECOND TERM
=> D = COMMON DIFFERENCE BETWEEN ANY 2 CONSECUTIVE TERMS
=> N = NO. OF TERM
=> S = SUM
=> SN = SUM OF N TERMS
_____________________________
=> WE HAVE GIVEN THE THIRD TERM
STEP 1 :
=> USE FORMULA OF NO. OF TERM TO OBTAIN AN EQUATION
_____________________________
FORMULA :
=> T N = A + D ( N - 1 )
=> T 3 = A + D ( 3 - 1 )
=> 9 = A + 2D
_____________________________
CONDITION :
=> WHEN 5TH TERM IS SUBSTRACTED FROM 9TH TERM WE GET 6
______________________________
STEP 2 :
=> FIND 5TH TERM AND 9TH TERM BY FORMULA OF TN
______________________________
TN = A + D ( N - 1 )
=> T5 = A + D ( 5 - 1 )
=> T 5 = A + 4D
_____________________________
T9 = A + D ( 9 - 1 )
=> T 9 = A + 8D
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FROM THE THE CONDITION :
=> T 9 - T 5 = 6
=> A + 8D - ( A + 4D ) = 6
=> A + 8D - A - 4D = 6
=> 4D = 6
=> D = 6 / 4
=> D = 3 / 2
_____________________________
PUT D = 3 / 2 IN ANY EQUATION ,
=> A + 2D = 9
=> A + 2 * 3 / 2 = 9
=> A + 3 = 9
=> A = 9 - 3
=> A = 6
_____________________________
T 2
=> A + D
=> 6 + 3 / 2
=> 12 / 2 + 3 / 2
=> 15 / 2
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T3
=> A + 2D
=> 6 + 2 * 3 / 2
=> 6 + 3
=> 9
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T4
=> A + 3D
=> 6 + 3 * 3 / 2
=> 6 + 9 / 2
=> 12 / 2 + 9 / 2
=> 21 / 2
______________________________
REQUIRED AP :
=> 6 , 15/2 , 9 , 21 / 2 , ........
______________________________
HOPE IT WILL HELP U ....
THANKS .....
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