how many terms of the AP - 15 - 13 - 11 and needed to make the sum -55 explain the reason for double answer.
i know solution we get ans 11 and 5 equal to n just explane reason please its urgent
Answers
Answer:
Given AP is -15, -13, -11....
sum of "n" terms is - 55.
Sn =n/2{2a+(n-1)d}
-55=n/2{2(-15)+(n-1)2}
-55=n/2{-30+2n-2}
-55=n/2{-32+2n}
-55=n/2×2{-16+n}
-55=n{-16+n}
-55=-16n+n²
n²-16n+55=0
n²-11n-5n+55=0
n(n-11) -5(n-11) =0
(n-5)(n-11)=0
n=5, 11
Thank you
Answer:
As you know the answer is 11 and 5 so let's skip the solution.
we get 2 answers as 5 terms and 11 terms because this is a -ve to +ve A.P
hope you understand as when you add the first 5 terms you get
-15 + -13 + -11 + -9 + -7= -55 as an answer
but even when you add the first 11 terms I.e
-15+ -13 + -11 + -9 + -7 + -5 + - 3 + - 1 + 1 + 3 + 5 = - 64 + 9 = -55
this happened because -3 -5 & -1 got cancelled by their additive inverse 1,3&5
=> YOU GOT 2 ANSWERS BECAUSE NO MATTER WEATHER YOU ADD THE FIRST 5 OR THE FIRST 11 TERMS YOU WILL GET THE SUM -55 ONLY, BECAUSE OF
THE NATUR OF THE A.P I.e of -ve to +ve