Question

if 3rd term of an A.p is four times the first term and 6th term is 17 find the A.p

Answer 1

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ANSWER :

AP IS 2 , 5 , 8 , 11 , ............

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BEFORE I START TO EXPLAIN THE ANSWER ,

=> SOME CONCEPTS U MUST KNOW ABOUT AP ARE :

=> T1 = A = FIRST TERM IN AN AP

=> TN = LAST TERM IN AN AP

=> T2 = SECOND TERM

=> D = COMMON DIFFERENCE BETWEEN TWO CONSECUTIVE TERMS

=> S = SUM

=> SN = SUM OF N TERMS

=> N = NO. OF TERMS

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GIVEN :

=> 3RD TERM IS 4 TIMES THE FIRST

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=> 6TH TERM IS 17

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STEP 1 :

=> TO FIND T3 , T1 , T6 BY FORMULA

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FORMULA :

=> TN = A + D ( N - 1 )

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PUT THE VALUES :

=> T3 = A + D ( 3 - 1 )

=> T3 = A + 2D

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=> T1 = A

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T6 :

=> T6 = A + D ( 6 - 1 )

=> T6 = A + 5D

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STEP 2 :

=> PUT THE NO. ACCORDING TO THE GIVEN QUESTIONS .......

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ACCORDING TO THE GIVEN CONDITION :

=> T3 = 4 * T1

=> A + 2D = 4 * A

=> A + 2D = 4A .................. 1

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STEP 3 :

=> PUT T6'S FORMULA IN THE GIVEN INFO

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ACCORDING TO QUESTION ,

=> T6 = 17

=> A + 5D = 17 .................... 2

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STEP 4:

=> FIND D BY MAKING EQUATIONS :

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=> SUBSTRAT 1 FROM 2

A + 5D = 17
-
A + 2D = 4A
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=> 3D = 17 - 4A

=> 4A + 3D = 17 ....................... 3

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=> ADD THOSE EQUATIONS 1 AND 2 :

A + 5D = 17
+
A + 2D = 4A
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=> 2A + 7D = 17 + 4A

=> 2A - 4A + 7D = 17

=> -2A + 7D = 17 ................,.. 4

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MULTIPLY THE EQUATION 4 BY 2

=> 2 ( -2A + 7D = 17 )

=> -4A + 14D = 34 ....................... 5

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NOW ,

=> ADD THE EQUATIONS 3 AND 5 ,

4A + 3D = 17
+
-4A + 14D = 34
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=> 17D = 51

=> D = 51 / 17

=> D = 3

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NEXT STEP :

=> FIND A

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PUT D = 3 IN T6

=> A + 5D = 17

=> A + 5 * 3 = 17

=> A + 15 = 17

=> A = 17 - 15

=> A = 2

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NEXT STEP :

TO FIND :

=> AP

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AP :

=> A , A + D , A + 2D , A + 3D ,.......

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AP :

=> 2 , 2 + 3 , 2 + 2*3 , 2 + 3*3 ,...........

=> 2 , 5 , 8 , 11 , ..........

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THANKS .......

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