Question

Find the number of terms in the AP. -6, -11/2, -5,......, of which the sum is -25. Explain the Double Answer.
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Answer 1

Answer:

n = 5 and 20

Step-by-step explanation:

first term = a = -6

common difference = d = -11/2-(-6) = -11/2+6

=( -11+12)/2 = 1/2

given sum = -25

n/2(2*(-6)+(n-1)*1/2) = -25

n/2(-12+(n-1)/2) = -25

n(-24+n-1)/4 = -25

n(n-25) = 100

n^2 - 25n - 100 = 0

(n-20)(n-5) = 0

n = 5, 20

Answer 2

Step-by-step explanation:

a1= -6 , d=1/2

sn = n/2{2a + (n-1)×d}

-25=n/2{2×(-6)+(n-1)×1/2}

-50=n{-12+1/2n-1/2}

-50=n{-25/2 + 1/2n}

-100 =n{-25+1n}

-100= -25n+1n²

n²-25n+100=0

n²-20n-5n+100=0

n(n-20)-5(n-20)=0

(n-5)(n-20)=0

n-5=0 , n-20=0

n=5 , n=20