Question

Find four consecutive terms in an A. P. whose sum is 88 and the sum of the 1st and the 3rd terms is 40.

solve full sum please

Answer 1

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GIVEN :

SUM OF 4 CONSECUTIVE TERMS IN AN AP :

=> 88

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1ST TERM + 3RD TERM :

=> 40

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TO FIND :

=> THAT 4 CONSECUTIVE TERMS

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SOME CONCEPTS U NEED TO KNOW ABOUT AP :

=> A = T1 = FIRST TERM IN AN AP

=> T2 = 2ND TERM

=> D = COMMON DIFFERENCE BETWEEN TWO CONSECUTIVE TERMS ( T2 - T1 OR T3 - T2 ETC...)

=> S = SUM

=> SN = SUM OF N NO. OF TERMS

=> N = NO. OF TERMS

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STEP 1 :

=> TO DETERMINE THE TERMS

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D = T2 - T1

=> T2 = T1 + D

D = T3 - T2

=> T3 = T2 + D

D = T4 - T3

=> T4 = T3 + D

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LET,

=> FIRST CONSECUTIVE TERM :

=> A - D

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SECOND TERM :

=> T1 + D

=> A - D + D

=> A

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THIRD TERM :

=> T2 + D

=> A + D

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FORTH TERM :

=> T3 + D

=> A + D + D

=> A + 2D

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STEP 2 :

=> TO GO WITH THE CONDITIONS

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ACCORDING TO CONDITION ,

=> A + A - D + A + D + A + 2D = 88

=> 4A + 2D = 88

=> DIVIDE BY 2 :

=> 2A + D = 44

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STEP 3 :

=> TO FIND A ( T1 )

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ACCORDING TO SECOND CONDITION ,

=> A - D + A + D = 40

=> 2A = 40

=> A = 40 / 2

=> A = 20

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STEP 4 ;

=> TO FIND D

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PUT A = 20

=> 2 * A + D = 44

=> 2 * 20 + D = 44

=> 40 + D = 44

=> D = 44 - 40

=> D = 4

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STEP 5 ;

=> TO FIND ALL TERMS

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FIRST TERM :

=> A - D :

=> 20 - 4

=> 16

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SECOND TERM :

=> A :

=> 20

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THIRD TERM :

=> A + D :

=> 20 + 4

=> 24

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FORTH TERM :

=> A + 2D

=> 20 + 2 * 4

=> 20 + 8

=> 28

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SO,

=> THE 4 TERMS ARE ,

=> 16 , 20 , 24 , 28

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THANKS .....

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