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The sum of the 4th and 8th terms of the ap24 and the sum of the 6th and10th term is 44find the first 5trem of an Ap |
| Answer» N :The sum of the 4th and 8th terms of the AP is 24 and the sum of the 6th and the 10th term is 44 , find the first 5 terms of the AP.Given :Sum of 4th term and 8th term of the AP = 24.Sum of 6th and 10th term of the AP = 44.To find :First 5 terms of the AP.Solution :Let the common difference be d and the first term be a.Case I :First let us find the nth term of the 4th term and 8th term.nth term of the 4th term :We KNOW the formula for nth term i.e,Where :tn = nth terma1 = First termd = Common Differencen = No. of termsHence the nth term of 4th term is nth term of the 8th term :We know the formula for nth term i.e,Where :tn = nth terma1 = First termd = Common Differencen = No. of termsHence the nth term of 8th term is Now according to the question , the sum of 4th term and 8th term of the AP is 24.i.e,Now by substituting the values 4th term and 8th term in the above EQUATION, we get :⠀⠀⠀⠀⠀Eq.(i)Case II :First let us find the nth term of the 4th term and 8th term.nth term of the 6th term :We know the formula for nth term i.e,Where :tn = nth terma1 = First termd = Common Differencen = No. of termsHence the nth term of 4th term is nth term of the 10th term :We know the formula for nth term i.e,Where :tn = nth terma1 = First termd = Common Differencen = No. of termsHence the nth term of 8th term is Now according to the question , the sum of 6th term and 10th term of the AP is 44.i.e,Now by substituting the values 6th term and 10th term in the above equation, we get :⠀⠀⠀⠀⠀Eq.(ii)Now by subtracting Eq.(ii) from Eq.(i) , we get :Hence the common difference of the AP is 5.Now putting the value of Common Difference (d) in the Eq.(i) , we get :Hence the First term of the AP is -13.To find the First 5 terms of the AP :First term :First term of the AP is -13.Second term :Second term of the AP is (a + d) i.e, ==> -13 + 5==> -8Hence the second term of the AP is -8.Third term :Third term of the AP is (a + 2d) i.e, ==> -13 + 2(5)==> -13 + 10==> -3Hence the third term of the AP is -3.Fourth term :Third term of the AP is (a + 3d) i.e, ==> -13 + 3(5)==> -13 + 15==> 2Hence the fourth term of the AP is 2.Fifth term :Third term of the AP is (a + 4d) i.e, ==> -13 + 4(5)==> -13 + 20==> 7Hence the fifth term of the AP is 7.Thus , the first 5 terms of the AP are , -13,-8,-3,2,7 . | |