Question

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.​

Answer 1

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