How many terms of the AP : -15,-13,-11...... Are needed to make the sum -55? Explain the reason for the double answer.
Answers
Answered by
196
given AP -15,-13,-11,...
first term=a=-15
common difference=d=a2-a1=-13-(-15)=-13+15=2
Sn=-55
n/2[2a+(n-1)d]=-55
n/2[2*(-15)+(n-1)2]=-55
n/2[-30+(n-1)2]=-55
n(-15+n-1)=-55
n(n-16)+55=0
n^2-16n+55=0
n^2-5n-11n+55=0
n(n-5)-11(n-5)=0
(n-5)(n-11)=0
therefore
n-5=0 or n-11=0
n=5 or n=11
sum of 5 term and sum of 11 terms = -55
here we two values
because we have positive and negative numbers in the AP
so u can get sum of first 5 terms =-55
and sum of 11 terms =-55
first term=a=-15
common difference=d=a2-a1=-13-(-15)=-13+15=2
Sn=-55
n/2[2a+(n-1)d]=-55
n/2[2*(-15)+(n-1)2]=-55
n/2[-30+(n-1)2]=-55
n(-15+n-1)=-55
n(n-16)+55=0
n^2-16n+55=0
n^2-5n-11n+55=0
n(n-5)-11(n-5)=0
(n-5)(n-11)=0
therefore
n-5=0 or n-11=0
n=5 or n=11
sum of 5 term and sum of 11 terms = -55
here we two values
because we have positive and negative numbers in the AP
so u can get sum of first 5 terms =-55
and sum of 11 terms =-55
Answered by
32
The answer is in the attachment
$$$Hope it helps$$$
Attachments:
Similar questions