Question

2
How many
tams of the AP 16,14, 12...
are needed to give the sum 6o? Explain
why do we do
get
two answer.
​

Answer 1

Step-by-step explanation:

Sum=S=60

a=16

d=-4

S=n/2(2a+(n-1) d)

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

60*2=n(32-2n+2)

120=n(34-2n)

120=34n-2n²

2n²-34n+120=0

(Dividing each term by 2)

n²-17n+60=0

(solving the quadratic equation)

n²-12n-5n+60=0

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

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

n=12 or n=5

We get two answers because the difference (d) is -2. Hence the sum of first 5 terms=16+14+12+10+8=60

and sum of first 12 terms =16+14+12+10+8+6+4+2+0+-2+-4+-6=60

If you notice the numbers 6,4,2 have there negative values in the first 12 terms hence the get cut and give you two values.

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