2)
How many terms of the A.P. 16, 14, 12, ... are needed to give the sum 60? Explain why do we do get two
answers.
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Answer:
In the given sum,
a=16
d=-2
n=?
Step-by-step explanation:
Sum(n terms)= n/2×{2a+(n-1)d}
60= n/2×{32+(n-1)(-2)}
60= n/2×(32-2n+2)
60= n/2×(34-2n)
60= 34n-2n²/2
60×2=34n-2n²
2n²-34n+120=0
n²-17n+60=0
(factors are -20,+3)
n²+3n-20n+60=0
n(n+3)-20(n+3)=0
(n-20)(n+3)=0
n=20 or n=-3
We get two answers as quadratic equation is formed but we discard or not consider -3 the answer as there can't be negative number of terms
So, n=20
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