Question

how many terms of the AP:16,14,12,... are needed to give the sum 60? Explain why do we get two answers I got ans 5 and 12 plz explain why do we get two answers

Answer 1

We know that Sn = n/2(2a+(n-1)d)

60 = n/2(2*16+(n-1)(-2))

120 = n(34 - 2n)

120 = 34n-2n^2

n^2 -17n+60=0

n^2 -12n-5n+60=0
n=5 or 12.


Here, we get 2 answers because of a quadratic equation giving both +ve values.

Answer 2

Answer:

n=5,12

Step-by-step explanation:

16,14,12

sum=n/2{2a+(n-1)d}

60=n/2{2*16+(n-1)(-2)}

120=n{34-2n}

120=34n-2n2

n2 -17n+60=0

n2 -12n-5n+60=0

n(n-12)-5(n-12)=0

n=5,12

Here, the common difference is negative therefore terms go on diminishing and 9th term becomes zero. All terms after 9th term are negative. These negative terms when added to positive terms from 6th to 8th term, they cancel out each other and the sum remains same.

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