How many terms of AP. 17,15,13,11,..... Must be added to give a sum 72
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In the above A.P., a= 17
d= 15-17= -2
s= 72= n[2a+(n-1)d]/2
Substituting values of a and d
72= n[2*17+ (n-1)-2]/2
144= n[34- 2n +2]
144= 34n- 2n^2+ 2n
-2n^2 +36n- 144=0
divide throughout by 2
-n^2+ 18n - 72=0
Now solve the quadratic equation.
-n^2+ 6n+ 12n-72=0
n(-n+6) + -12( -n+6)= 0
(n-12) (-n+6)=0
Therefore possible values of n= 12 and 6
The double answer is due to the fact that the value of d is negative.
The sum of 7th to 12th terms of the AP would be 0.
Hope This Helps :)
d= 15-17= -2
s= 72= n[2a+(n-1)d]/2
Substituting values of a and d
72= n[2*17+ (n-1)-2]/2
144= n[34- 2n +2]
144= 34n- 2n^2+ 2n
-2n^2 +36n- 144=0
divide throughout by 2
-n^2+ 18n - 72=0
Now solve the quadratic equation.
-n^2+ 6n+ 12n-72=0
n(-n+6) + -12( -n+6)= 0
(n-12) (-n+6)=0
Therefore possible values of n= 12 and 6
The double answer is due to the fact that the value of d is negative.
The sum of 7th to 12th terms of the AP would be 0.
Hope This Helps :)
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